It is not normal. I have moved a hitch that originally came off a 93, from my 87 to the 95, thence to the 99, all without trouble. It's a Mopar OEM receiver, by the way.
However, you may find that it's pretty easy to tweak the hitch rails back and forth either on purpose or by accident. If, for example, someone dropped it wrong while off the vehicle, it could be enough to put it out of alignment. You can probably bend it a little to fit again.