I think people don't actually understand the meaning of "broken" cards. A card can be very powerful and NOT be broken. Back in the day, Dr. Boom was a fantastic card, but not even close to broken. Broken cards are ones that utterly alter the meta in ways that are either unfair or unintended (such as the broken Wretched Tiller combo in Wild a while back). Broken cards (or combos) frequently have very high winrates AND have few, if any, counters.
Nothing priest has right now is even within spitting distance of broken. And the class's winrate proves it.
I'm by no stretch a priest main, but I play it from time to time and I cannot believe I'm hearing people complain about it. By no stretch of the imagination is priest in good place right now. Control Priest a tier 2/ tier 3 deck that has decent matchups against some of the major meta decks, but is only heavily favored versus hunter. It also, BTW, is one of the only decks that can keep secret pally under control.