yes, they would kick out people paying them lots of money to get in. There certainly is no incentive in a pure capitalist university to keep rich well paying people enrolled.
Correct - aggregate reputation is more valuable than individual tuition payments. It's simply a matter of maximizing value. Western universities kick out tuituion-paying students all the time, for many reasons.
That would imply that the university would also be honest.
It doesn't have to be intellectually honest (my god, saying this about a "university"). It can merely value the increased revenue (assign bonus targets if greed is the only available motivator). Though we ought to hope for more.
Did you know that in America most private schools are worse at educating students than public schools?
This article isn't about America - corruption, violence and bribery isn't how grades are determined here. India has different problems and requires different solutions.
Are you aware of the self-organization of private schools in India (and other poor countries) that parents prefer? Even very poor parents find a way to pay for their children to avoid the government schools there (the schools are very cheap by Western standards).
Have you heard Malala Yousafzai talk about government schools in the region? It's a disaster from top to bottom.