It actually does: Indian Railways, Coal India, Air India (until very recently), State Bank of India, Bharat Petroleum, BSNL, the list goes on and on.

I think the relevant figures here would be how much of each countries' banks' balance sheets are de facto liabilities to the state. I can buy that Chinese banks incur more liability for their government than Indian banks do for theirs; I don't buy the idea that China is 100% liable for its banks' balance sheets while India is 0% liable for its banks' balance sheets.