I agree with most of your points, but I don't think #1 (family-centric society) is the problem, or even a direct driver of corruption. If you were referring to nepotism, then I think that exists all over the world. An overall corrupt climate just makes it easier to practice nepotism.
I know nothing about India but the "family-centric" stuff is easier to understand as a problem if you phrase it "clannish". And that is actually a huge problem in some areas.
Its a problem because if you don't ask for a bribe, you're selfishly throwing away money you could you use help out your cousin just out of fear of getting punished. And in India you probably do have some cousin who needs the money because their car broke down/their child is getting married/whatever.