You ask if access to prestigious gard & post-grad institutes is "merely a question of access to resources." Obviously, it is not merely; the question to ask is "if it is significantly influenced by access to resources."
And surely, we do see more rich and middle class kids than poor ones. Please check how many students in IIMs and IITs ask for subsidies. The stats are available with most instis.
Now compare the income profile in the IITs/IIMs with the country's profile. Do you see a difference?
Thus, I think the stats do establish that there is indeed a correlation b/w family income & access. Clearly, this is not the only factor, nor does it establish causality. (Such stats tests do not.) There may be connexions using other variables such as access to primary and secondary education, access to coaching, etc.. but those are hypotheses, to be validated.
