I found the opinion to be quite thoughtful and interesting, but I ultimately wasn’t persuaded (despite the recent United States v. Stevens precedent, on which the court heavily relies). The court’s theory seems to suggest that, while fraud is constitutionally unprotected, attempted fraud is protected, at least so long as no-one who relied on the attempted fraud can be identified. And it also seems inconsistent with the Court’s acceptance of false-light invasion of privacy claims — see my brief for more details on those cases — which rest neither on a specific well-rooted false light invasion of privacy exception nor on any plausible judgment that the false light tort passes strict scrutiny. (Note that the Court has treated the imposition of civil liability for speech much the same as the imposition of criminal liability, so I don’t think the false light cases can be distinguished simply on the grounds that they are tort cases and not criminal cases.) Because of the false light cases, and various others, it seems to me (and I so argue in my brief) that the relevant First Amendment exception is a general one for knowingly (or recklessly) false statements of fact, albeit with some narrow exceptions-to-the-exception, and knowingly false factual claims of having received a medal would fall into that.
But in any event, the court took a different view, and it will be interesting to see what the Tenth Circuit does, since I expect that the government will appeal.
UPDATE: Note that my analysis assumes that the Stolen Valor Act would be interpreted as limited to situations where the display of a medal would be understood as a statement of fact, rather than as fiction, hyperbole, humor, or parody. But I think that’s a sensible interpretation, and one that a court could easily apply as a clarifying construction of the statutory element of “falsely represent[ing]” oneself as having gotten a medal.