On some motors, they are side specific. The GenIII Hemi is one, they are machined for a certain side.
But on the LA motor like yours, the heads can go on either side. The intake then blocks the rear coolant ports in the intake face of the cylinder head so coolant only flows out the ports on the front of the motor. If the blockage was in the back of the head when it is on the passenger side, it wouldn't be much of an issue because coolant doesn't flow out of the head there in that situation. But if the cylinder head was then swapped to the other side, now coolant that needs to flow out of the head and into the intake headed to the radiator can't and would cause an overheating problem.
You might poke your finger into the outer most ports on the intake face on the junk cylinder head, or maybe shine a flashlight in there. You might find something different between the two, with the right one being the suspect one.