Did you look at the study?

I'm biased to pile on too social science studies but the study in question made efforts to address these considerations.

From another article [0]:

  "On average, scouts and guides were 15 per cent less likely to 
  have developed mental illness or depression by middle age, 
  even those from poorer backgrounds whose initial risk was higher."

[0] http://www.telegraph.co.uk/science/2016/11/10/scouts-and-gui...

Wealth correlates with parental involvement but not at 1.0 - in other words, if parental involvement is a confounding variable (most likely given its established effect on mental health), correcting for wealth won't eliminate it.

Who's disagreeing with you? I'm lost as to what you're responding to.

"the study in question made efforts to address these considerations"

I'd argue that they didn't make enough efforts.

Are you assuming that or did you look at the research paper?

"We used variables collected at the appropriate sweeps of the NCDS to control for childhood factors which might affect...."

... snip ...

"Family aspiration was estimated from parents desire that their child leaves school at the minimum age, asked at age 11."

There was no judge of parental involvement beyond whether parents had a desire for their children to go to university or get A-Levels.