I've often worried about a "right-wing" patsy attempt like that happening. In that case it wouldn't be for PR purposes but to send a message to the target and his allies "we can get you at any time AND make you take the blame". Just enough plausible deniability for a media coverup. It would make about as much sense as the Jan 6th scam that they ran with for months. Those left wing nut jobs would be even more crazed because they'd be able to feel morally justified that a right-winger did it.