I can see how adding too much capacitance to a regulator could cause the regulator to oscillate, but oscillation in tube amplifiers is rarely due to the power supply, and when it is, it's because the power supply has inadequate regulation (too high an output impedance), not the other way around.
Yes, obviously changing capacitor values in the amp itself, and particularly in the feedback circuit, can cause an amplifier to oscillate. I spend a fair amount of time reading DIY audio sites (and building my own amps and preamps), and I don't think I have seen a case where adding a small amount of additional capacitance to a coupling cap or power supply cap ever caused an amp to oscillate.