As an Indian I often wonder, the real question is not why India is so corrupt(esp. at the lower levels of bureaucracy), rather how come certain countries have zero corruption at those levels? Perhaps I'm too pessimistic about human nature.
China is interesting in this respect, on the one hand corruption is rife, on the other it is nominally totally out of bounds and the punishments are severe. I don't understand how those can both be true at the same time without a huge amount of selective enforcement.
My experience with India to date has one of utter amazement at the brashness and the degree to which corruption has infused society there. I suspect that for India a part of it is that it has social classes that are very disjoint. This creates a very fertile growth medium for corruption because it puts a lot of small people in positions of relatively large amounts of power over the lives of others.
For example in the UK, if one were to write a history of corruption-fighting there would be three big strands since the 1500s. Religion: the replacement of a church that sold salvation with (sometimes extreme) Protestant moralism. Military: at one point commissions in the army were bought and sold. This practice was replaced with more meritocratic promotion in order to win wars. And financial: English law seems to be considered one of the world's fairest regimes for contract law, and is often used for contracts between non-English big companies.
You definitely need a few people who are weird and unreasonable to start it off though. Have you seen the movie Serpico? I thought that gave a good portrayal of how odd and antisocial the people who cause that kind of change often are (and the real story was more so e.g. his marriage collapsed as part of the process). If we're going to be really speculative, maybe it takes an individualistic culture to even have that kind of personality?
This applies to direct corruption. There are different, structural kinds of corruption though, like "old boy networks" where business may get handled via personal relations. While still damaging for the society, it probably isn't even illegal in most cases.
I think many people in India, who consider themselves to have morally 'good' - wouldn't bat an eyelid while offering bribes. They don't get push back from peers either. What irked in India is when you try to do the right thing - i.e. not take the corruption shortcut - my peers would tell me I'm stupid or naive or something to that effect. In the US if I say that I attempted corruption, my peers will probably tell me I'm morally depraved. So you need a critical mass of people that enforce and most people just follow along.