Dumb social science researchers again as usual lol - correlation != Causation. Sigh. The parents who are likely to push their kids and do helicopter parenting are unlikely to be unemployed or living in trailer parks. They're likely to be in successful careers with great networks. Might that explain the success of their kids to a greater extent? Of course.
Are you sure that you didn't compare it with other employed reasonably well to do parents? While I agree it is a lot easier to be a social scientist than a STEM researcher, but I dunt think they can be that dumb