This is one of those things that seems to have come from a long-forgotten corner of the internet. At the same time though, it carries with it no risk of repeating and might help save some expensive parts. Given that there's no downside, it's probably a good idea not to let your parts sit and dry with the degreaser on them. It's possible that in certain situations a specific interaction between a degreaser and the finish on some parts will cause discoloration. Not immediately but if allowed to sit and dry on the part.
There could be a million reasons the whole scenario is completely made up. Specific formulations of cleaners will change over time and bike parts are always evolving. On the other hand, it makes sense not to allow chemical cleaners to sit on parts long term. It only takes a few minutes for a good cleaner to do its job. After that, thoroughly rinse everything.