Yes, there is a huge current account deficit (export/import imbalance) and that is a big part of it.
However, as the agency that manages the circulation and control of the currency, ultimately I look at the RBI as the 'face' of the Indian Rupee.
That said, the government doesn't have to trust bitcoin. However, regulatory burden in India is extremely high regardless of the kind of business you want to start. India ranks poorly on several 'Ease of doing Business' indexes. [1] I'm bringing this up since you mentioned the start up industry. It's just not that easy to start something in India.
Yes, tax evasion is a huge problem in India. But that's a cultural thing. The government has made it very hard to evade taxes (as long as you rely on existing banking channels) for now, but it doesn't really stop anyone. I can imagine that they are afraid that people will launder money by exchanging cash directly into bitcoin. However, why doesn't the government then go after the real estate business in India that normally takes 30%+ of the money in cash ? It is extremely hard to buy properties in resale unless you agree to pay a large percentage in cash. Oh wait, the government likes to put their black money into real estate.
For the same reason as Real Estate, I highly doubt that the Indian government will ban bitcoin or make it illegal. They have plenty of money they would like to sink into this new genius asset class. They might however make it harder for regular people to get into it.
Besides, you can always wire money to bitstamp and buy bitcoins as much as foreign exchange controls would let you.