...The real ground is one of the 2 vertical (not D-shaped) prongs on the plug. I have several times seen the true ground come loose, and some equipment will quit working (as it should), while other equipment starts using the protective ground!...
This is wrong !!! The "vertical prongs" are the hot and neutral, the "taller" one, on the left, being the neutral. Neutrals and grounds are bonded in the main panel, but never in any panel remote from the main. Since the neutral is carrying power if a load is connected, it is no longer at "ground" potential at the load end due to the voltage rise that is an inevitable consequence of the resistance loss of the power wire when current is flowing through that wire. A couple of volts above ground is quite common. The ground lead (the "D"-shaped one, by itself), since it
generally does NOT carry any amount of power, remains at ground or zero potential. There is current in that ground *ONLY* during a fault condition, which could include a faulty piece of equipment that has some amount of leakage current into the ground path. This is why I suggested that condition in my first response as a possible source for the hum that the OP is trying to eliminate.
...Were you to disconnect the protective ground in such a situation, in all likelihood the chassis of your equipment would be hot.
Not necesarily. If the neutral comes loose then the equipment connected to that outlet should stop functioning, period! There should NEVER be a situation where power is passing through the ground connections EXCEPT in a fault condition, in which case it is indeed there to protect the living soles who might come in contact from that equipment who might otherwise find
themselves a part of the return path. Since the chassis of the equipment is not designed to be part of the power path, it will only be hot in a situation where the equipment itself becomes faulty, e.g., develops a short from a powered portion of the circuitry to the chassis AND the ground connection of the equipment has also been removed. That's the whole purpose of that equipment having a ground connection, and the primary reason why you should NEVER defeat that ground path by using a 3 to 2 prong adapter without giving that adapter a proper ground...