I have found AMEX to be rather wishy-washy on the ability of a merchant to require ID. So their old slogan about "not leaving home without it" should include "and an acceptable form of ID."
I have found MasterCard to be much better in that aspect. On their
form, one of the only four issues that can be submitted is the merchant required ID. It might not be a bad idea to keep this handy.
Fry's Electronics is the business I have had problems with ID on. Every time I have refused ID, it has been necessary to escalate it to a supervisor (and even higher sometimes). Eventually I have always been successful, but it is frustrating that the store continues to blatantly violate the merchant agreement (of which I am a third-party beneficiary). I believe that 99+% of customers submit without any push-back since each cashier I have dealt with acts like I am the first one to ever have refused.