The low-voltage secondary winding is between the primary and the high voltage secondary, in the PT-10. It is thus capacitively coupled to both, but when grounded it serves as a Faraday shield between them. Thus the noise on the power line does not get passed into HV power supply and the signal-handling circuitry. By draining the power-line noise current directly to safety ground, it does not pass through the signal ground wires, where it would induce hum into the signal.
In addition, the heater is capacitively coupled to the cathodes of the tubes; if the heater supply were not grounded it would induce common-mode hum into the signal.