The only discussion there is about how to calculate the capacitor assuming that a simple CR circuit is sufficient.

What they don't consider is whether or not a a simple CR circuit is sufficient.

From the diagrams provided, you should be able to see that there may be issues with a simple CR circuit:

if the supply voltage has a slow or otherwise "dirty" rise;

during a "brown-out";

if the supply voltage has a slow or otherwise "dirty" fall.

These are the kinds of things that Richard is looking into...