Strategically it doesn't make a lot of sense to lynch him today. If he's legit he dies tonight anyway if he's not we lynch him tomorrow.
Now let's say I were Mafia. Great, we don't lynch Priz today. I don't kill him during the night and then you guys are going to lynch him tomorrow because he didn't die? Mafia can easely choose to kill someone else especially after your post.
Seeying wether he dies tonight is not a valid reason to not lynch him today or to lynch him tomorrow.
If he's legit and we waste a lynch on him its kind of like giving the mafia a free kill since they would have had to target him anyway.
Any mislynch is a free kill for the Mafia. The doc being no exception.
And if he isn't legit there are probably more than 1 anti town killing roles between the mafia/assassins/3rd parties who could target and kill him anyway. If that is the case we've killed an anti-town without even wasting a lynch
So let's not lynch people because the Anti-towns could kill him? Great. Let's not lynch me. Cop claims are pretty favoured for a kill, so if you think I am bad just let the other killing parties take care of me!
And ofcourse there aren't that many killing parties out there that would kill Priz. As I said, if he were Mafia then the Mafia wouldn't target him. The tribunal council wouldn't risk it and also Priz is in the council. The assassins guild hasn't killed in two days, so I doubt they'd kill him. But if Priz is anti-town this is the only Faction that can kill him at night.
I doubt there is actually another third party out there that can kill.