GD,
Here is where I am having a problem.
The controls are inside a metal furnace along with the sensor itself and the related wiring.
Where / how is any kind of 'noise' being introduced into this equipment that an EGC would fix?
If I seem to be a bit of a PITA about this it is only because the OP is asking for an answer and IMO we have only provided anecdotal stories about what might be.
Last attempt:
A furnace, depending on its size (residential ... multistory large school) has a bunch of electrical components in it that define the electrical "noise" environment:
1) Electric ignitor transformer.
2) Electrically operated valves (pilot, main, safety).
3) Electric draft fan(s), electric purge fan(s); warm air blower fan(s), circulation pump(s).
4) Electronic controls (or heaven for fend -- electromagnetic).
5) Electric Flame Detector (case in point).
1) runs at a high voltage until pilot lights.
2) controlled by electronic controls.
3) may be timer controlled from controls, pre-ignition; thermostatic control.
4) sit in the middle
5) tries to detect small currents
Now the goals:
1) Don't blow up the building: Make sure that gas doesn't flow in any appreciable amount before you have an ignition source and for not long thereafter if no flame is detected.
2) Heat the building when the building system calls for heat.
3) Don't burn down the building: Shutdown the system if an over-temperature is detected.
The electronic flame sensor walks a very narrow path electrically.
IT MUST SHUTDOWN ON FLAME MISSING. It has better not shutdown when flame is present.
Without proper grounding, the electrical noise from the furnace: motors starting, high-voltage sparks from the ignition transformer and external electrical noise can overwhelm it.