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.