One thing I’ve noticed, in browsing a subreddit where people share their dogs’ DNA breed test results, is that people can sometimes be quite resistant to accepting a finding that their mutt contains only a very small percentage of “Breed X,” when said mutt happens to have inherited some particularly dramatically visible trait associated with “Breed X.” For example, a dog who has a merle coat pattern, or whose coat texture is wiry-scruffy with facial bearding. Both those traits are dominant or co-dominant and caused by just one gene, so even a tiny amount of ancestry from a merle or wiry-coated breed could be sufficient to cause them if the portion of DNA inherited from that ancestor happened to include that gene. But they’re also both very “loud” traits visually, and that loudness can trick us into assuming that there must be “a lot” of some merle or wiry-coated breed in there. And once you’ve gotten that idea into your head, it can be easy to then proceed to convince yourself that your mutt “clearly” also shows other, more vaguely defined and/or multi-gene traits associated with that breed, like “high energy” or “feisty” or “fast” or “leggy”–these are all pretty relative terms, and someone with years of experience in a breed commonly described as having them may understand them quite differently than the average person.
Also, even within most pure breeds, there’s sufficient diversity present in the collective gene pool to yield individuals who may be quite far off the norm or ideal for that breed (as epitomized by show or field champions) in both looks and behavior. Sometimes this gets read simply as that individual being a “faulty” example of the breed, other times it may lead to accusations or suspicions that the individual isn’t really purebred. There can be characteristic variations within lines, too; for example, German Shepherds bred for police work are as a group likely to display a somewhat different balance of behavioral and perhaps physical traits than those bred for seeing eye dog work, which in turn will look and act somewhat different than GSDs bred for show ring success. Backyard-bred and puppy mill dogs of a given breed, who generally haven’t been bred according to any selection criteria at all–just “whatever two dogs of this breed I happened to already own”–are especially likely to display variation from the breed standard, because standards are meant to define an ideal that breeders must keep continuously and rigorously selecting for; they aren’t meant to summarize all possible individuals that could result from the genetic diversity naturally present in the breed.