Note 1: The ferrite coils used in output filters have to have capacitors on both sides (electrically speaking) of them to reduce the ripple voltage substantially. If you only have one cap after the ferrite coil, you'll gain little compared to not having that coil to begin with (EDIT: This may not be true of all PSUs for a very strange reason - scroll down to post #5 for the explanation), as you'll just end up with the ripple current going through the coil and capacitor after it, only reduced a bit (as what else is there to complete the loop the ripple current takes through the circuit???). (The ferrite coils are much smaller than the mag-amps in inductance as well as physical size.) Having a complete filter indeed keeps the output ripple voltage much lower, but that's because the cap before the coil completes the ripple current loop, so the coil and the capacitor after it only draw a small ripple current, giving a very low final ripple voltage with good caps.
(I haven't actually sourced this statement, but it would seem to me that the unimpressive +12V ripple result on that Rexpower unit is indicative. You can see in the photos that +12V there has a decent coil, but only the one cap. My recommended solution would be to use higher grade replacement caps in filtering stages with only one cap and/or no ferrite coil.)
Note 2: On 100/120Hz ripple, from the primary side - having multiple outputs on the same transformer means there will be some level of it on all but one of those. (It can't reach the outputs of the buck converters used for +3.3V and +5V in modern units, nor those of the linear regulators sometimes used for the negative rails.) It just needs to be kept at a safe level, which is the sole responsibility of the PSU engineers. The secondary-side components won't have any appreciable effect on that frequency, unless you install some ludicrously huge (in µF) caps.