Reading this thread motivated me to dig up the rules online, and this bit struck me:

"The individual with a disability has been trained in the use of the service animal and is responsible for all handling of the animal. Consequently, carrier personnel and other passengers should not attempt to pet, play with, direct, or in any way distract service animals."

So if you aren't allowed to ask whether it's a service animal, are you allowed to infer that it's not because the individual with the disability is not capable of handling it? That certainly seemed to be the case here.

Of course the FA's were technically in violation of this regulation for interacting with the dog, eh?

So if UA decides to compensate the other pax partially with miles, can they deduct them from the offending passenger's account?