Your assumptions and your logic are faulty.

Assumption: Food isn't rotting in India. Google: 'Rotting Food India'

Your logic: Corruption/Theft doesn't change the price of a commodity. You are forgetting that the government has already bought the commodity. Now it is being sold again. This drops the price (still too expensive for the poor) which means that those who can afford food buy at a lower price.

Lower Price = Less Supply

This is elementary because the rice is being supplied once but sold twice. Therefore the farmers are being paid half of what they deserve.