For the states that don't recognize the "non-resident" permit, what state is the driver's license issued from?
That will settle the residency matter. If your friend has a NY driver's license and an AZ permit and is in a state that doesn't recognize non-resident permits things could get a bit troublesome. So, the answer to your question is, "No."
Each state is free to do as they wish, within the guidelines and framework of already established law, and the Constitution. Not recognizing an out of state or non-resident permit is pefectly within the bounds of the law.