Minor hitch. Inter-branch incidents like this happen in the US military all the time.
NSG is not a military branch. It's under MHA, and a joint command couldn't have done shit until MHA called in the military.
There is. You need a ballsy prime minister. Indira Gandhi achieved more without a tri-services command (breaking enemy-state number one apart into two equal parts in a military conflict), than the US ever did with one.