Well, here's the problem - now we're actually trying to read into a bullshit story.
Simply put, the Jews had no such authority and needed to persuade the Romans to off anyone who was a serious threat to them. And yes, that's right - the high priest was appointed by Rome. This does, however, put a gigantic hole in the story, because his appointment could be pulled at any point and if he had in fact incited a riot and threatened Pilate, as the Bible says he did, he would certainly have put him on bad terms with Roman authorities, who throughout their history had shown no problem with stomping the shit out of people who caused problems and could easily just have sliced the whole lot in two.
Jeff