*DNA has proven conclusively that the dingo breeds (both Australian and New Guinea) originated from Asian domestic dogs. Their basic origins are not in dispute. Here are some of the studies confirming this fact.
*Domestication does not dissolve after just a few thousand years, which is a blink of the eye in evolutionary terms. See Dollo's Law for further explanation.
*Dingoes follow the precedent set by mustangs, pigs, ferrets, and other feral domesticates. See "feralization" for further detail. Ferals can absolutely survive without human intervention, as seen in cats, ferrets (in NZ), horses, pigs...all that is required, is for the animal to not be out-competed by other species.
*Dingoes never return to the wolf (the animal they are undisputedly the domesticates of, and can freely interbreed with) Other domestic dogs also never return to the wolf: if left without human interference, they return to the archetype of dingoes.
*Here are some of the domestic traits retained by both AU and New Guinea dingoes: 20% smaller brain size as compared to their wolf ancestor; reduced flight distance and adrenal response (see studies on neural crest development and domestication syndrome--here is an overview); changes in pigmentation (such as white markings and solid coat colours, vs wild canids which are agouti); faster social and sexual maturation; changes to reproductive patterns; reduced fearfulness as compared to the wolf; some curl to the tail; smaller size than the parent animal; inherent tendency for eye contact with humans; affinity for humans (do not need to be pulled early and bottle fed); inherent ability to follow a pointing finger, as a dog instinctively does (but not a wolf).
This pattern is followed by domesticates in general; it's not specific to canids.
*Dingoes breed like domesticates, not wolves. The wolf has a short, inflexible breeding season, and can breed only once per year. It is rare for females other than the alpha female to breed. In dingo "packs", all fertile females will breed, and population control is effected by infanticide (killing the pups of subordinate females). Both Australian and New Guinea dingoes have an extended "preferred" or typical breeding season, and Singers can also come into heat multiple times in the same year, especially if they didn't conceive during their first heat. (This is the same breeding pattern that feral cats follow.) Unlike wolves, male dingoes are often fertile year-round. Pups are hazed and driven away as early as 4 months of age, and become sexually mature much earlier than wolves as well.
*Dingo DNA falls within the spectrum of the other domestic dogs. While they can be distinguished by specific markers, so can other dog breeds. We can tell a malamute from a husky, in roughly the same way we can tell a dingo from a husky.
*Landraces and formal dog breeds are both created by the same mechanism: a combination of genetic isolation from other (usually European) breeds, and a population bottleneck from limited foundation stock. "Wild" dingoes are a feral landrace.
*There are no behaviours found in dingoes, that are not also found in some dog breeds. The preferred or environmentally prompted annual breeding season, lack of repetitive barking, physical flexibility, ability to climb trees, regurgitation of food, and so on, are all present in some other dogs as well.
*There are no physical features found in dingoes, that are not also found in some dog breeds. See photos below for some illustration.
*The genetic signatures, behaviours, and physical traits are not only overlapping with domestic dogs, but are also notably distinct from those canids which evolved apart from humans, such as coyotes and wolves.
*A portion of both the AU and NG dingoes have been back under some degree of human influence for hundreds of years, and under strict human control for decades--much like other primitive dogs such as the Basenji, Jindo, Shikoku, Canaan, and Carolina Dog.
*Any animal, through natural selection and epigenetics, will "customise" itself to its environment. Dingoes are no exception. The archetype of the pariah dog is an evolutionarily ideal model--it is "what works" for canids under those living conditions. Left to its own devices, Nature has created a similar animal on every continent except Antarctica...as evidenced by the multitude of other pariah dogs, which actually outnumber man-made purebreds!
*Dingoes are still Canis familiaris in their homeland, despite hopeful media opinions claiming otherwise. This is due to a lack of solid scientific evidence, and a rejection of poor quality "evidence" such as the Crowther study. Additionally, since dingoes can and do interbreed freely with other domestic dogs, they are clearly the same species in any meaningful sense.
There is plenty of legitimate research establishing the effects of domestication, and the genetic lineage of the dingo. The only things that create its classification controversy, as opposed to that of mustangs or sheep, are the political repercussions of protecting a scientifically and culturally valuable animal who nonetheless is a threat to ranchers, and the emotional baggage and egos associated with Man's Best Friend. A solution could easily be devised to protect the interests of all, without resorting to scientific inaccuracy. After all, (invasive) foxes are "wild", but are still killed as frequently and cruelly as dingoes. If "wildness" did not politically save the fox, why would it save the dingo?
Australian farmers could take a page from the history of the North American wolf, whose successful management included things like conditioned taste aversion, and livestock guardian dogs, llamas, and/or donkeys. One might even consider the approach to feral cat management, where animals are trapped, sexually sterilised, and re-released--these animals hold the territory and social breeding rights, while the population decreases over time. Adult dingoes provide guidance to the upcoming generations, teaching them to hunt desirable prey (including invasive foxes and cats who decimate the native wildlife, and kangaroos who quietly consume large amounts of vegetation needed by other species) instead of setting themselves upon "easy" livestock meals due to poor success in taking their natural prey.
Domestication also does not disqualify dingoes as a mere "invasive species". Europeans and their livestock have only been in AU for about 200 years (the true "invasive species", from an ecological standpoint), whereas dingoes have been there for at least 4000 to 6000 years...and probably much longer, as they have such strong genetic ties to the New Guinea Singers and the land bridge went under between Australia and New Guinea 6 to 8 thousand years ago. (However, it would definitely be less than 10,000 or so, since there have never been dingoes in Tasmania.) Dingoes, regardless of heritage, are still Australia's apex predator, and have been so for long enough to be recognized as such instinctively by their prey. Bilbies will hide from the scent of a dingo or other dog's feces...but not from that of feral cats, a much newer predator with only a couple hundred years' interaction. Dingoes could be managed as any other wildlife, or even declared a National Treasure, like the primitive Japanese breeds or the Korean Jindo. It's unconscionable to drop thousands of wooly cheeseburgers on the floor of the his home, and then get pissed if the dog eats some of them. One might cull the most troublesome, willful dogs who won't be run off...but not dump 1080 poison everywhere, try to exterminate an entire species, kill lots of innocent bystander species in the process, and wreak havoc on the environment...all because you can exploit an animal's politically-charged classification.
The political argument that 'dingoes should be declared nondomestic' makes the mistake of implying that domesticated animals are worthless, and only wild animals have value. This is missing the fundamental basis that make dingoes and other dogs so amazing! Wolves and coyotes are "just another wild animal". The dingo, as the Original Dog, is the sole surviving representative of our co-evolution with Canis lupus. He is a wealth of heritage and information! Dogs, and most especially the free-living archetype dogs, are something very special indeed--and even more worthy of preservation.
UPDATE:
Here is another paper that gives a detailed explanation on the heritage of the dingo, and its appropriate classification as a domestic dog.
The Wayward Dog: Is the Australian native dog or Dingo a distinct species? Jackson 2017
http://www.mapress.com/j/zt/ article/view/zootaxa.4317.2.1/ 12247
In light of these conclusions, and taking into account the recommended current practice for taxonomic nomenclature of the domesticates, as embodied in Opinion 2027 of the ICZN (2003), recent attempts to treat each of the Australian Dingo and the New Guinea Singing Dog as distinct species of canid are clearly unsupportable.
Dingoes and New Guinea Singing Dogs are feral Domestic Dogs and, as such, they must be treated taxonomically as breeds or varieties of C. familiaris.
Furthermore, as feral domesticates, neither variety can be recognised taxonomically as a subspecies, irrespective of whether or not they can be diagnosed by any combination of morphological, behavioural and genetic characters.
And one more: The Dogma of Dingoes, 2019
PHOTO comparisons of primitive breeds:
New Guinea Singing Dog: 
Desert dingo: 
Alpine dingo: 
(It's been said that there may be more
phenotypic distance between different varieties of Australian dingo, than from
dingoes to other similar pariahs!)
Korean Jindos: 
INdogs: 
Canaan dog: 
AfriCanis: 
Carolina Dogs: 
Kishu Ken: .jpg)
Shikoku: 
Jomon Shiba Inu: 
(Shibas come in the same 3 basic colours as the dingo): 