It's only a crime if the person actually wears the medals or uniform (Title 18, Section 702 & 704). Making the claim isn't a crime or claiming to be a veteran. And pretty common to find people claiming to be veterans, especially on the Internet.
And you aren't going to get Veteran's benefits without a valid DD-214. Not that the VA doesn't goof up. They had like over a hundred veterans on the books claiming prior POW status to get extra benefits from Desert Storm. And their were only a handful of actual POWs.
Congress right now is trying to pass a law that will make punishment for wearing unearned awards have a harsher penalty. I don't think it includes false claims to being a veteran.
Of course the military already harshly punishes soldiers who illegally wear awards. The navy just sent a corpsman to jail for a year or so for doing it.