Hopesmom, 
A service dog handler cannot be asked their disability, as you said.  A Support dog can be asked and you must have a statement from a llicensed professional regarding the specific task the dog performs for you.   
Granted, some places may not ask, but they are allowed and see documents.     
It is just a little tricky if you get in the thick of it.  I had to drive to Chicago one time to pick up someone who had a support dog that was half way through her airline trip from California, who got checked for her support dog and did not have the appropriate paperwork and she could not continue her trip. We got it taken care of but with a 12 hour delay and a couple of missed flights.   A statement from a psychiatrist and a trainer are the best things and then the dog must behave well, too, of course.     
				__________________  .      Cali    , and Cali's keeper and staff, Jay No, not a "mini" Yorkie - She loves to motor in her Mini Cooper car          |