It's a crime to threaten people. It's a crime to lie to the police. It's a crime to impersonate law enforcement and doctors.
The First Amendment may give you the ability to say anything, but when what you say furthers a crime, then you should be arrested.
The crime here isn't for saying he's a soldier who was given the medal of honor. It's for pretending to be one. What he said is just the evidence of the crime.
For that to apply, we need to have an actual law against impersonating a soldier. Currently there is not one. And even then, wouldn't it be similar to the crime of impersonating a police officer and would only apply if that person were actually trying to perform the duties of a solider? I mean let's say you're at a bar and meet a woman and you work at McDonalds but tell her you're a police officer, that is NOT illegal. BUT if you pull that same woman over for speeding and tell her you're a police officer, that IS illegal.