The back of a pot used as a signal ground, in a grounded chassis design; how reliable?
What they're doing is using the chassis ground as a signal reference, instead of using a signal reference plane or bus that is connected to the chassis ground in an explicit manner.  This seems to work OK at first, but creates not only the problem you're describing where you have signal grounding wires making unreliable connections to the chassis, but a much nastier gremlin: common-impedance coupling.

Since the signal return currents are now flowing through the same piece of metal as all the 60Hz and RF circulating currents the chassis has picked up, these changing currents can cause voltage drops between different "signal ground" points, which manifests in the circuit as funny noises.

The fix for this is to lift all the signal ground points from the chassis and connect them to a signal ground reference point, bus, or plane, which is then connected to the chassis at a single point near where the signal inputs and outputs are found.  This keeps circulating currents in the chassis from inducing voltages into the signal ground system, and also means that the integrity of the signal reference system isn't dependent on weird mechanical connections, such as those you saw in potentiometer cases.