If only reality worked that way!
Currents flow in loops period, and voltages are measured between two points, all else flows from this and ohms law.
Draw the current loop from the output of a stage to the input of the next stage, AND BACK, that second bit is the trap, because something like a non inverting opamp does NOT have a ground connection, so the question is how does that current close the loop? This is what those caps to ground provide, a way to close the current loop that does not go half way around the board and share all sorts of doings with other signals.
That 100+dB PSRR is also usually a low frequency number, it may or may not exist at high frequency, depends a bit on how the thing was compensated, but for most opamps it falls with frequency.
I do wish opamp vendors would actually tell us which power rail the Vas integrator was referenced to, it would be helpful to know sometimes. You can make a guess based on differences in PSRR between the rails, but it is just a guess.
This stuff is amenable to spice simulation BTW, just include reasonable parasitics, it can give some quite cool insights.
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