As abhorrent as it is that some people lie to gain honor and respect they have not earned, having the courts rule that lying is a crime takes us in a direction that we probably don't want to go.
We already have a category of laws that deal with lies that lead to material harm: "Fraud".
Do we really want the government making the telling of an untruth into a criminal act? I don't think we do.
The proper way to deal with folks who steal valor is through public censure and debunking; to have laws that limit what those people can say implicitly creates a situation where we are all "under oath" at all times, in a de facto way. Once the bureaucrats figure out they have that power, any mistake or misstatement we make, about anything at all, will become a potential pretext for criminal investigation.
We don't want to go there.