How is it possible that the output tubes burn out when the left and right gnd are connected at the input?
There must be some other problem with that amp.
A number of amplifiers (not just tube IME) lift the input ground for isolation, stability, and to prevent ground loops (which I could have lumped with "isolation"). I had an expensive (ARC) component that did that, and if you shorted the RCA inputs to chassis ground, it would oscillate. Since the oscillation was well above the audio band, your first clue was overheated plates and blown tubes. Internally there was a very small (0.5~1 ohm IIRC) resistor from RCA jack shield to main signal ground.
One other datum is that tube amps (and of course any bridged amps) do not necessarily ground the speaker terminals so care must be connecting to anything but speakers. My ARC amp tied the 4-ohm output terminal to ground, for instance. I learned this the hard way decades ago when I added a nice external speaker power meter that shared a common ground. Fortunately, a squeal and blown fuse saved the amp from my ignorance. These days problems can arise when adding a sub via speaker-level inputs if the sub does not isolate the signal and ground lines connecting to the speaker outputs.
FWIWFM - Don
