Can someone draw the circuit / current flow that requires an EGC from the panelboard be present at the furnace?
I'll describe the operation:
1) The gas pipe or orifice form one end of the "one wire" detector.
2) A rod is positioned where the flame ought to be, it is connected to the "one wire".
3) As I understand it a "high" voltage AC is applied the "one wire" and the current is monitored.
4) If the flame is present, a DC current flows from the "one wire" to the detector.
5) If the flame is absent, no DC current.
6) If the "one wire" is shorted AC current is present.
7) Only DC current is the flame present condition.
8) This signal is very small.
9) History: Flame rectification hearkens back to very early radio.
If the gas pipe is not well grounded, noise is picked up by the detector and things are flaky.
This has been my experience. I learned this at the knee of a very good HVAC guy and I have fixed these problems typically when the furnaces over flamed and melted the control unit or 3rd-party contractors didn't bother to connect good grounds.
Since it has to do with a wire it is often considered the electrician's fault.
The plan is not to leave the gas valve open when there is no flame -- sometimes known as a air-fuel bomb.