Doesn't 'home life' depend on the parent's emphasis on physical activity, sports, or general fitness? I.e. if the parents put a higher value on other things, it seems likely that the children will follow their lead.
Parents chaperoning their kids every hour of every day _is not normal_ and never has been, except in the US.
I disagree. Stress from a dysfunctional family or timing demands from being required to act as a caretaker, among other things, will decrease the time and energy required to pursue physical activity.
And physical fitness, high enough to stimulate the indicators they measured, involves more than just causally playing outside - though my interpretation of that sets quite a low bar for the physical exertion involved.