My Lexie goes everywhere with me. She is a seizure alert dog for me. There is no training involved with this--they either have the ability or they don't. I always make sure that I have her ID tag on her with a vest, or at least the tag is attached to her carry bag. I've never had a problem once the tag is seen.
And yes, its true according to the ADA one is not to be questioned about validity of the service dog, your medical/psych condition.
Lexie's Mom