I think I understand microphonic tubes in the signal chain, but I don't understand why a microphonic rect tube would cause problems? If the filter caps filter out the 120Hz AC(or rather pulsing DC), why wouldn't the filter caps also filter out any microphonic noise/signals the rect. tube "picks up"?
The first filter cap works with the rectifier, and takes what is essentially a very large, pulsating d.c., and filters out
some of the pulsations. You get essentially a large d.c. output, with an a.c. output superimposed on it, but the a.c. component is smaller than what it was with a rectifier and no filter cap.
The choke/resistor and the next filter cap do the same: reduce (but not eliminate) the a.c. component. And so on with the successive filter caps. At each filter cap, you can measure some amount of a.c., even if it is very small by comparison to the d.c. So you almost never have pure d.c. unless you have some form of regulator, though we do strike a balance with having "clean enough" d.c. at each stage.
Microphonic noises aren't hum, though. Especially in the case of a rectifier, the likely microphonic noise is a short, sharp impulse and can be very large.
Further, caps need time to charge/discharge. The bigger the cap or the impedance of the supply, the longer that charge/discharge takes. If you mess with the Duncan PSU Calculator, look at the plot of output voltage, paying particular attention to the beginning of the plot. You'll see the supply voltage ramp up as the first filter stage charges up.
So, sudden microphonic impulses (assuming they aren't as severe as an actual intermittent interruption) are really beyond the capability of the filter caps to filter out. That's why when you have a microphonic rectifier tube, it tends to sound like odd scratchiness or rattling that's akin to a speaker problem. Since it's output is no so much a sound that gets amplified, but a disruption of the supply voltage/current to every other stage in the amp, the sonic effect is different than, say, a microphonic preamp tube.