While she was abusing the policy, the law is clear that he can't ask her that, because of repeated violations of the ADA by private and public property owners. You can't decide whether it's a service dog.
I do not believe this is an accurate statement of the law. Federal regulations and DOJ publications have convinced courts generally that the ADA prohibits public accommodations from requiring proof that an animal is a service animal, but I have found nothing in the ADA or related federal regulations (e.g., 28 CFR s. 36.104 and 36.302(c)) that says that a public accommodation cannot inquire as to whether an animal companion is a service animal.
You are correct to point out that "stress dogs" can qualify as service animals, provided they have some specialized training. (E.g., Rose v. Springfield-Greene County Health Dep't, 668 F. Supp. 2d 1206 (W.D. Mo. 2009)).
Frankly, the only time I'd see a dog as being an issue in a public accommodation is a restaurant, hospital, or any other establishment that may be dinged for health code violations.