I am somewhat not agreeing with your very last sentence though.
If smart kids from depressed backgrounds tend to find a way in, then I assume that statistically spoken, the smart kids from depressed backgrounds are either not proportionally correctly represented in numbers, or there are statistically speaking fewer smart kids in the population group coming from depressed background.
If the first were true, then it would means that there is no equal access or opportunity for them to get in, if the second were true, it would mean "depressed backgrounds" would have a genetic impact on your "smartness" genes. Well, I can't live with either of these conclusions.
Unequal access or opportunity comes in many forms. Children of affluent parents will go to college even if they are not as bright as many from working poor backgrounds who do not. There is also "white privilege" even if overt racial discrimination is not there, and so on. You shouldn't think of equal opportunity as either existing or not, because then you have to conclude either that it does not exist, or you find yourself blaming victims of social inequalities for their "free" bad life choices. Neither conclusion is acceptable, nor does it follow from the analysis. guaranteed to evoke a violent reaction from police is to challenge their right to "define the situation." --- David Graeber citing Marc Cooper