That’s not the law.
You are free to lie; not free to defraud.
The question here is whether stolen valor is “speech” and, if so, fraud.
The name of the act, "Stolen Valor", is somewhat misleading. A soldier who legitimately demonstrated valor in the service of his country can't have his valor stolen...nor his intelligence, honesty, or any other character trait. The coward who falsely wears decorations and awards is "stealing" or misrepresenting the material commendation (i.e ribbon or medal) received for the valor.
If you think of "valor", like intelligence, as a type of human capital, I think it's easier to see how this does bleed into the area of fraud. I suspect you generally agree with intellectual property protections. People don't wrongfully appropriate somebody's intelligence or thoughts, but rather the written, diagramed, representations of those thoughts which they then portray as their own. Similarly, one doesn't "steal valor", but represents another's (the real winners of such awards) as their own.
It may not be as marketable in monetary terms, but it is still personal capital. Can you mention one instance where a person would misrepresent themselves as a medal winner where it was not for some type of personal advantage?
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.