I certainly agree with you there, however, it still does not prove that it is a hoax of his doing. As a trauma surgeon, he has reasons for being anti-gun, especially with him having been a victim of gun violence on top of it.
If they can match the flier to a printer that he has access to, then that would be strong enough evidence to most likely secure a conviction. The system being what it is you never know what a verdict will be anymore with a case.
There’s nothing to charge him with since he never went to the police.
Which itself is VERY strong evidence in support of a hoax.
If he believed there was a real threat, he goes to the police and files a report so it can be tested for fingerprints and otherwise forensically examined.
His behavior is wholly inconsistent with perception of a real threat.
I admire the stubbornness of your skepticism, but it is no longer reasonable to be skeptical. If he filed that report he’d go to jail for a false report, and that is why there is no police report.