I wonder how hydrogen peroxide (a strong oxidant) can reverse the yellowing of plastics, if the yellowing is the result of oxidation. I'm not a chemist, but this doesn't seem to make sense.
Interestingly, The idea that the yellowing is from the Brominated Flame Retardants in the plastic is actually itself a myth. It's a sort of believable just-so story because people look up bromine, see it is brown, and go "ah, makes sense". The interaction doesn't actually involve the brominated Fame Retardants, and is a breakdown of the butadiene chain of the plastic polymer which is effectively an oxidization which is catalyzed by energy (whether light (UV being the most energetic), or Heat). This happens with All ABS plastics, including those that don't have any Tetrobromobisphenol-A. This is why UV Stabilisers and absorbers tend to be a common inclusion in the formula of ABS plastic. (And why when they are forgotten/omitted you see things like car recalls due to seatbelt fasteners degrading). The yellowing is effectively the molecular debris from that breakdown, which gives a colour to the plastic. Hydrogen Peroxide is a strong oxidizer- it works in retrobrite not by reversing the process, but actually speeding it up. It reverses the colour change because while it significantly speeds up the butadiene being broken down, it also breaks down the molecular debris that results from it, to smaller, colorless compounds. It will also interact with other compounds in the plastic- for example, those that might have been added for the factory colouring.The result is that the colour of the original plastic returns- possibly without any factory set colouring compounds as well. Another downside is that because the butadiene chain is still compromised, retrobrite can never restore the structure of the plastic, so it will remain brittle. I've seen suggestions that an acid might be able to chemically recompose the butadiene polymer. I was able to successfully test a paste of Oxalic Acid, without any sunlight exposure for example- though it took a week and the colour change was very small.
This might explain why direct sunlight can brighten plastic instead of yellowing it even more.
In a way, its good it works that way. It doesn't strip off the apple logo or "mac" lettering or whatever.
Your theory is reasonable but it seems its actually breaking down a bromine based fire retardant. Bromine itself is kinda gross brown color and some oxides like dibromine pentoxide are clearish-white so its quite realistic that hitting it with an oxidizer clears things up.
I wonder if it has anything to do with sodium perchlorate in the dishwasher tabs, the heat of the dishwasher or both.
TL;DR: Over time the bromine based flame retardants in retro-era plastics degrade (hence the yellow/brown colour) and H2O2 plus some energy (UV light/heat) can be used to reverse the process.