As a point of reference, in my 1500+ nights at Starwood/Marriott and 1000+ nights at Hilton, a large fraction of them on Corporate Rates for clients or other associated companies, I have NEVER been asked to produce a company ID nor have I ever been asked to produce an AAA or AARP card. Now maybe I look honest, but I don't understand what all this fuss is about.
I have many fewer nights ... and have been asked more than once. Is it common ... no, not at all. But when it happens you better have an ID on you or another form that shows your eligibility.