So you know i'm both a big supporter of our vets, and of dogs as well. But... If the dog was being difficult in any way, the owner does have the right to ask them to leave. Now the things that he said made me think he's just a douche, but there's a chance that the dog was too energetic or spastic that day, particularly if the vet was having a bad day.
Other funny thing is that there is 0 requirement in the americans with disability act for the dog to be certified or for you to carry any sort of paperwork with you showing they are a service dog. you can just say "he's a service dog" and if the dog isn't a pain in the ass, there isn't anything a business owner is supposed to be able to do.
I support the charity Battle Buddy, you guys may want to check it out
http://kennys.battle-buddy.org/
they help provide service dogs for vets with PTSD. Really great idea