I have only heard of a few occurrences of paint becoming affected. Personally, I have only seen it once and that was with a 1987 targetmaster (gun guy) when his face went a paler shade of red.
Aside from that, all painted figures have come out just fine, an example that I can think of now Vroom. His paint actually came out cleaner and brighter! That's probably due to a lot of the dirt and crap on the surface being dissolved by the H2O2 which was probably a safer thing than wiping it with a cleaning agent.