The reality is that they are in charge of their entrance rules for crossing into the United States, so the Americans will make their decision on who's eligible to come in and who is not.
The point I was making in my remarks is that if there's a dispute that you run into at the border, you're in a better position to explain yourself if you have a piece of paper that lays out your status on the Canadian side as opposed to not being able to at all contest the impression of the U.S. border officer, which may be “you're lying to me”. One of the most difficult circumstances a person will face in crossing the border is when the officer on the other side thinks they are dealing with a liar. That's the problem that having a piece of paper to explain your status would help you address.