bugeyes, yes, that is the working theory, anyway. Pin 4 on each tube is that channel's Voltage amplifier input, and the Volume Control simply attenuates the signal getting to Pin 4. At least, that is what the VC is supposed to be doing!
Give those grounds a serious inspection; I cannot think of a likely mode of failure in a step attenuator that could cause the issue you describe without there being a problem with the ground somewhere.
So, you are going to want to check for continuity from the "ground" terminal of the appropriate VC section to the middle terminal of the nearby terminal strip, for starters; then, you'll want to make sure that middle terminal strip terminal has a good connection to the ground buss wire that runs through its bottom hole.