that anecdote leads to the same conclusion

not quite. your claim was that with a bad situation at home, school does not make a difference. while i understand the opposite. the worse the situation at home, the more of a difference school makes for them.

i see it like this:

    good home + good school = good outcome
    good home + no school = good outcome
    
    bad home + good school = ok outcome
    bad home + no school = bad outcome

so for a good home school does not matter. for a bad home it does. (i am ignoring bad schools, they probably make things worse in either case)