What is the purpose of a turntable's ground wire?
This is my take on the turntable and amplifier circuit.   







simulate this circuit &ndash; Schematic created using CircuitLab

It looks like the ground wire is important in this schematic.  

The turntable motor chassis will float at about Vsupply/2 if not grounded, and the environment will have other nearby objects with 60 Hz voltages on them. These couple to the tone arm and then cause currents to flow in the signal wire, to earth. This current gives rise to a voltage, because of the finite resistance of the signal wires. At the amplifier input, it will see a voltage which is both the pickup voltage, and some of the environmental buzz.

The ground wire earths the chassis of the turntable, mainly the tone arm, to reduce this voltage. Its resistance is lower than the signal wires, but more importantly, it earths the chassis, which is then weakly coupled to the signal wires. So if the environmental "hot" object is at ~60 V, Vsupply/2, the tone arm might also float at 60 V AC, which might induce a few uV onto the signal wires because of their resistance. With the earth wire connected, because of the fairly low (and independent) resistance of the earth path, the environment might manage to induce only a fraction of a volt on the tone arm and chassis. This has to pass through the stray capacitance onto the signal wires, so the effect is much reduced.

Connecting the earth wire to the RCA cable shield at the turntable might help a bit, but it forces this induced current to flow on the cable shields, which will transfer some voltage to the signal path.

It is my firm belief that all EMC / shielding / ground loop voodoo can be reduced to simple circuit schematics, as long as all ground paths, capacitive coupling and external sources are included.
This one is a quasi-DC problem, everything is just as you see it, a combination of L, C and R. There are no wavelength-effects, so it should yield to conventional analysis.