I think that what you are saying here doesn't necessarily serve as a counterpoint to the GP's point. Rather, it's only an additional piece of evidence. Where GP referred to things like a parent being sick serving as a downward pressure in the effort to improve one's circumstances the point is one of externalities which are not typically accounted for.

And in this case, the externality you're bringing up is that oftentimes being raised poor means you're being raised in an anti-intellectual environment. And that externality is something that a lot of poor people have to deal with.

It's another instance in which the game appears to be rigged against those from a poor background.