The voltage across the capacitance between the fan switch leg when it's at 120V and the LED switch leg will produce some amount of current through the LED. There does not have to be any load current on the fan switch leg for that to occur. And so the theory that both of you are proposing might still be true. It could be interesting to experiment with a length of Romex and an LED bulb to see if such blinking can be induced, and if so, what length of cable would be required. I can't do it because Romex is not commonly available in the Chicago area. A convenient excuse.