No, you do not automatically get a low priority queue punishment. If you were a "leaver" when a remake happens, then you simply get flagged by Leaverbuster. You got the punishment because you have been flagged by Leaverbuster too much. That's how it works.
Also, how do you know the people who say that then leave the game don't get punished? If they do it often enough, they will get punished by Leaverbuster, and there is no way to know if they have received a Leaverbuster punishment unless you manage to find them streaming. A Leaverbuster punishment is impossible to track through 3rd party websites, and even if you report them, you will not receive a notification that they were punished if it was given by Leaverbuster.