The point is that the U.S. is fully capable of having a political relationship with entities it doesn't recognize as a sovereign state.

Take Taiwan as another example. Both the context and details are completely different from that of the PNA, but it nonetheless contradicts your premise in the same manner.

Mandatory Palestine certainly existed. Although you may argue it wasn't a country, because it was under the administration of the British.

The current State of Palestine exists, and is recognized in many forums, although not by all participants; but it doesn't have de facto sovereignty as it's essentially occupied.