Here is an example of why you should never run temp probes into the cooker through the door. The result was a super hot spot that burned the meat where the probe wire caused an air leak.
Is this true on pellet stoves only or does it include stick burners?
The doors on the stick burners are much heavier and can damage probe wires easily. Pellet cookers work on positive air flow and pressure, so causing an air leak in the door is detrimental and can cause severe hot spots. In a wood pit, the air "draw" is from the firebox to the chimney, so creating a leak in the door with probe wires can also be detrimental to the heat/fire management.