In this cases, I think "non-extreme cases" basically means "the child manages to survive until the age of psychological maturity with no debilitating injuries". The claim is that the main role of parents is just to get the kid to adulthood in one piece, and anything else is extra and might not seriously help or harm commonly measured outcomes. One might add the assumption that the parents at least didn't actively inhibit ordinary non-parental exposure, to rule out things such as never learning to talk or something.

(But remember, I'm not claiming this at all, just stating what I think the real claim is. I don't even think the more conservative version is correct: even if you assume that childhood experiences with parents controlling-for-differing-non-parent-related experiences aren't that important, how could variations in ongoing parental support in adulthood possibly not make a difference?)