I don't recall any Hilton asking me for my AAA card either (several Marriotts have), although I'm sure there are some that would. None of the properties ever noted the account number or even if the card was current but just wanted to prove membership.
There are times during my senior moments remembering my account number just doesn't happen so I just enter 430 as the international club number and still see the AAA rates. Given anyone can enter anyone's number, asking for the card at the front desk is an acceptable request. I carry too many cards as it is, but AAA is one I make sure is part of the inventory.