It's also why the Chinese are interested in Iran and Russia. Land-based oil. As well as the South China Sea.
The point is that there is no major conflict of interest between China and India, and for that reason, both countries are more likely to cooperate and collude than being openly antagonistic. Hence it's unrealistic to believe that India will go out of its way to antagonize China just because the US would like to see that. India is too proud to be an American puppet.
Chinese and Indian collusion in recent oil field biddings is an example of the willingness of both countries to cooperate (and benefit together) rather than cut each other's throats and achieve a pyrrhic victory.
You're right,India maybe too proud to be an American "puppet",but it's not neither foolish enough to ignore the threat China has posed to India by itself & through proxies like Pakistan,Bangladesh & Burma/Myanmaar.The cooperation on oil will only go to an extent-both sides are getting to big for their boots to keep sharing like that.The F-16I or any other aircraft purchased will almost certainly have conformal fuel tanks for longer range,in order to complement the SU-30,which is the only Indian aircraft which can penetrate beyond Tibet into Chinese airspace.