Aside from the fact that stolen valor is scummy behavior, when used as a qualification, whether by a politician or a private person, it is false advertising. False resumes in the private sector often result in firing. Also, we have false advertising and false labeling acts for many products. Why wasn’t this issue raised when thinking about who is harmed by the lie?
Pretty sure those kinds of issues were raised, but the courts have said there are already laws against fraud that suffice to punish that behavior without further restricting freedom of speech.