You are also not free to defame, that is injure another with your lie. So, only if your lie does not defraud, or defame (libel if written, slander if spoken), are you free to lie without legal repercussion. Defamation can be either a civil or criminal matter.
It can be argued that real veterans, and real medal recipients are demeaned or defamed by the fakers, and so the law can protect them.
Personally I'd just as soon see the real ones beat the snot out of the fakes. Including of course John F'n Kerry.
I just think it’s too nebulous of a harm to be actionable.
By the same logic by “lying” (as defined by Al Gore) about Global Warming, you are harming every American by threatening our very existance!
I think this should be settled by an ass-whooping, not a law.