I think it's good that you are going with a private training facility for a couple of reasons. First, IN GENERAL, the training staff will be much more knowledgeable. Second, even after all puppy shots, I don't like my dog on the floor in Petsmart and Petco
. There is just no way for them to control who brings pets in and whether they have had all immunizations, etc. There was one day that I walked through and a woman had this dog in there who was so filthy that you could smell him in the next aisle!
Do make sure that you visit and watch a class at the place you are thinking of though. Just like I don't think you go to vets for advice on nutrition, Vets, in general, know even less about training. Make sure that the training center you choose, and the specific trainer you work with, uses positive training methods. No choke or prong collars, no yanking or snapping leashes... Will at least introduce you to clicker training, and uses LOTS of fun, positive (food and play) reinforcement with the puppies to start building a really strong relationship with them.
A good puppy K class will also include lots of off-leash play time, with mixed size/breed dogs so that puppies learn to get along with all kinds of other dogs. If it is well supervised, the trainer should be able to keep your little puppy safe and keep them from being traumatized, even if the majority of other puppies are large breed pups.
That said, while what the Petsmart trainer said was stupid (she should have kept her mouth shut if she didn't know the breed better) a person doesn't have to have an intimate knowledge of all the different breeds in order to be a good trainer. Dogs are dogs, and each is an individual. There are certainly some breed characteristics, but it can be a mistake approaching any individual animal assuming you know what they will be like based on the breed. Any specific individual might very much surprise you!