I totally agree with you about the First Amendment problems in the "Stolen Valor Act" per se; but since the MOH comes with a stipend and other government benefits, I think you could construct a law, similar to laws against impersonating an active duty soldier, or Federal Official, that would pass Constitutional muster.
I agree, pawdoggie, and especially if the person is attempting to both claim the MOH and collect the federal stipend and benefits.