I see both sides of this. Almost everyone knows my GSD is a GSD. They do think she is small (24.5 at whithers and 70 lbs is small), but she is always ID'd as GSD. I mean, there is no question.
A vet really should recognize the most common breeds because there are genetically associated ailments with different breeds, especially shepherds, labs or collie types (among others... there are plenty more, eg. bulldogs).
I don't care if people think my yellow husky (all sled dog) is a lab mix. He has floppy ears, is yellow, and I can understand it. I also don't care if my belgian malinois, who is long haired, is mis-ID'd. I can tell the vet what breed my dogs are, and don't expect them to guess with mixes or non-typical breeds.
But, Kira, like my GSD, really looks like the classic image of a German Shepherd. I would assume, if nothing else, that if the vet didn't know Kira's breed he can't have much experience with treating GSDs and that alone might be enough for me to look somewhere else.
Breed-specific understanding isn't a neccesity, but it is helpful. I go to a vet who specializes in sled dogs with my husky, and if I could find one with expertise in working shepherds, I'd go there with my shepherds. I've found it does make a difference. Plus, then the vet really likes your dog...
And the comment about her being "small" and "fluffy" kind of threw me off as well.