Yeah, but Veterans don't sport an old Active Duty Military ID, when they are no longer....Active Duty. It's like using a college ID years after you are out of school.
Again, veterans are usually registered with the VA and you get a Medical ID for VA hospitals/clinics. That's about the only ID I can think of, other than using one's DD214.
I think the restaurants use it mostly for advertising, to generate goodwill. They probably realize that most vets will have too much pride to come waltzing in and saying essentially "I'm here for my free meal." Not saying they should feel bad. Just saying how I see it.