Currently, yes, this is the rule, Shiny and HA Pokemon included. We actually agree here and don't think there's really a good in-universe reason for Rockets to have breeder perks (especially not those ones), but the rule predates us by many years and (we think) was originally added to give people more of an incentive to app a Rocket character.

This is something we're VERY open to changing and probably will once we dig deeper into how perks work for all the trainer classes, but with the rule having been in place for such a long time, we didn't want to yank it out from underneath anybody who was doing a lot of breeding with their Rocket characters without warning!