I think it's more a spectrum than a line. In any case, I don't understand why someone would draw such a line above "upper middle class mathematician/researcher/manager job at fortune 500 company", because they would be proven wrong trivially by looking at statistics of entrepreneurs historically. I would also distinguish "entrepreneurship" from what PG did, which was basically switch from interest to interest without an eye on how to monetize his education.
I think what you are calling intellectual background is a part of what is normally called class. Usually these sorts of things are correlated together, although as you point out, it's a trend, not a rule. PG also comments on this himself [1]:
> Closely related to poverty is lack of social mobility. I've seen this myself: you don't have to grow up rich or even upper middle class to get rich as a startup founder, but few successful founders grew up desperately poor.
I think what you are calling intellectual background is a part of what is normally called class. Usually these sorts of things are correlated together, although as you point out, it's a trend, not a rule. PG also comments on this himself [1]:
> Closely related to poverty is lack of social mobility. I've seen this myself: you don't have to grow up rich or even upper middle class to get rich as a startup founder, but few successful founders grew up desperately poor.
[1] http://paulgraham.com/ineq.html