Bathroom fan trips GFCI which doesn't protect it

I recently attempted to reduce the noise and vibration from a bathroom vent fan by putting small pieces of a rubber sheet between the fan's C clamp and the mounting box. Not long afterwards, when I turned off the fan a nearby GFCI outlet tripped. But the fan is not downstream of the outlet -- the fan still worked even while the outlet was tripped.
How can a device trip a GFCI when it's not downstream?
Is it a bad idea to leave the rubber in place? Could it cause problems since the fan would no longer be grounded to its mounting box? The fan is plugged into a standard two-prong outlet in the mounting box.
-Apr
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The GFCI is probably fed by an Edison circuit, sharing a common neutral with the fan's circuit. You can install a ground wire from the motor to the housing and keep the rubber in place

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snipped-for-privacy@hotmail.com wrote:

Maybe motor ground is floated by your mod. Install a piece of wire to ground motor well and see.
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