I interpret the phrase 'exotic pets' more loosely. I worked as a vet tech (small animals, not farm animals) for many years, and anything that was not a cat or dog was called an exotic. This included rabbits, hamsters, rats, snakes, parrots, ferrets, monkeys and various wild animals. The vets that worked on these animals were called Exotic Vets. It is an entire discipline in various vet schools. The ward where these animals stayed when hospitalized was called the exotic ward. So to me it is a phrase used in the pet industry that doesn't necessarily mean the literal definition of "exotic". We did have some chickens come in on occasion, and they were seen by the exotic vet and stayed in the exotic ward.
So to get to my point, I don't find it strange that the pet store called the chicken an exotic pet. But I think it is pretty stupid that they didn't allow the chicken into the store. They made a generic policy intended to keep people with "weird" and perhaps unpredictable animals out of the store - like monkeys or something.
As for never taking a pet into a store, although I agree there is some risk I don't entirely agree with the sentiment. Animals rarely come into direct contact with others with the exception of dogs sniffing each other. Also, in many of my own instances of bringing my dogs in, it was when I already had them with me in the car and I realized I needed dog food or something, and didn't want to leave them roasting in the car. I personally wouldn't want to bring a chicken into a store because most chickens would be freaked out by the experience, especially if there are dogs in the store. But if I were on my way home with a chicken or two in the car on a sunny day and needed to buy something I wouldn't hesitate to bring them in with me in a cage.
ETA: also, my dogs are exposed to WAY more diseases at dog parks than the pet store...