Oh no, they should!
however, if you pull up on a guy running down the road.. Are you going to just take his word that the guy he chasing is what he says he is?
I sure as hell would not shoot him based on someones word.
I would think that in this instance they not only recognized him, clothes, etc., that they had no doubt about who he was. I do think you are trying to make a point but not sure if you realize that it may be a bit silly.