Unfortunately, such laws apply to two things, IIRC:
1. Impersonating an active duty member in order to gain access to military-only stuff (access to a base, or to use a commissary or gain benefits, etc)
2. Falsely claiming to have won a medal. This one was added recently because there were a number of fraudulent vets claiming to have won the Silver Star and other such medals. IIRC, the law also applies to some service award devices such as combat infantryman badge.
I'm not sure why the law doesn't go further. Probably some pols are worried about old men who were 4F in WWII being carted off to jail.
Well, poster 'Roses Chealsy' from mil.com may have some cliam if she spent time & money on a son that never existed.