Safety Ground Q

I never really understood grounding until I watched the ASR video, assuming the information is correct, of course. Amir says the safety ground does absolutely nothing unless there is a fault in which the case becomes electrified and the safety ground would kick in. I think I got that right, but maybe not.  OK, so if the safety ground is doing nothing, why can lifting it eliminate a ground hum?  It seems the safety ground would have to be doing something other than waiting for a short if eliminating it reduces hum. Thanks.