Feedback thru the rails to the input stages can easily happen in simple discrete amps because the PSRR of say a CE transistor or CC tube stage + load resistor can't be any better than what's implied by the Thevenin equivalent of the device dynamic impedance in parallel with the load resistor voltage divided into the input impedance of the following stage. Which is usually garbage.
It can also happen in single supply op amp circuits when there's insufficient bypassing on the "virtual" ground which often is both defined by a voltage divider from the positive supply and "real" circuit ground and connected to one of the input pins via a feedback resistor and gets injected that way.
For this discussion I define "low frequency instability" to be say 1MHz or something within the gain-bandwidth product of audio op amps. HF is HF like the radio definition, 10s or 100s of MHz. Can an audio op-amp oscillate at 10s of MHz? You bet, but it can't be a round-the-whole-loop phenomena how could it? There's a compensation cap inside, the open loop input-to-output transfer function has a dominant pole at very low frequency, as a whole it has no gain way up there. The V->I stage can't possibly smash current in and out of the compensation cap fast enough to make it happen.
In this block diagram of an op amp where is the feedback loop thru the PS getting in to make it unstable at HF? It definitely can't be anywhere prior to the 30pF compensation cap:
They probably just used whatever they had a lot of/was cheap. For audio op amps the precise value of the caps likely isn't super-critical; anything between 10nF and 1uF might be fine depending on the specific part.
They sometimes put small ceramics in the 10s or 100s of pF in parallel with the feedback resistors, too, to well-define a high-frequency -3dB point for the stage.