Is this weird? “Service animal” situation

I’m just remembering that this happened and I’m not sure how to feel about it.

A student emailed me on the first day of class, about an hour before, asking if their service dog could be in class. I said Of course, is there paperwork with the accommodations office? Etc. He then replied that it’s not a true service animal because it’s a 10mo old puppy that’s just starting training. No paperwork, no vest, etc. So, I asked my chair because I’m always down to have a dog around but I know some students may be afraid of dogs. Chair says no, had to have paperwork done, be a real service animal, etc., which I assumed he’d say. Fine.

I let the student know and then after class they asked the same questions, so I sent them to the accommodations office because I’m just not sure about this shit.

I get an email later from the accommodations office saying paperwork is not necessary for service animals and he can bring the dog to class. I replied oh! Because he told me it wasn’t a service animal, and they confirmed it doesn’t matter.

I’m just confused. Can anyone just bring their pet to class? Can I bring my dog to work?!