I am a tenor, and can barely match a 60-Hz hum. 120-Hz, no problem.
Hum might be a characteristic of this set. It is transformerless and uses a voltage doubler B+ circuit. Voltage doublers have low ripple at zero load but relatively high ripple under load. When brand new, this set might have had noticeable hum. However, hum might also be caused by a fault which causes excessive B+ current to be drawn (such as insufficiently negative voltage for the grid bias).
More unlikely is that you have a shorted filter choke. You can check the choke by unsoldering one of its leads and measuring ohms across it- it should be around 185 ohms according to the schematic. If it's a lot less than that it possibly has shorted windings.
Found this on the philco repair bench
http://www.philcorepairbench.com/tips/svctip25.htm