Paranoia is a vicious beast - if you have an ID that displays information that you, for whatever reason, don’t want recorded - news flash, your home address is likely publicly available on your county tax records if you own your residence - then, you should use an alternate ID that does not display that information, such as a passport.

Refusing to provide ID physically just substantiates whatever reason, misguided or not, that was listed in the FDA training that the FDA is watching for.