That's a ridiculous "I just don't want to deal with it" answer. First of all, they absolutely can, BY LAW, ask if a dog is a service dog. Under the ADA you can ask if the dog is a service animal that is required due to a disability, and what type of work or task the dog has been trained to do. The ADA only prohibits them from asking about a person’s disability.
And in the case of dogs in tents, their own website says this right now...
"Please note: Pets are not allowed in pop-up trailers or tents."
https://disneyworld.disney.go.com/faq/rooms-packages/camping-pet-friendly/