I've never had this problem at any reputable rental agency. I've rented specialty cars from all of them, never provided airline information. I've also rented at my home airport (I live 30 miles away) hundreds of times over the course of 20 years. Used all of the big agencies at one point or another.

I had a problem once at one of the disreputable rental agencies, but that's off-topic here.

Of course, National has all of that info about me already. They don't have the insurance information about my personal car but they do have a credit card on file for me that provides secondary rental insurance coverage. If anything, I can see them validating your CC coverage if you decline their coverages. But if they're doing that at all, they're doing it behind the scenes using my CC number.