Choking someone out underwater?

Close to the end of the movie Bond was fighting with one of Silva's henchmen out on the lake and then underwater when they broke through the ice. The henchman was choking Bond out in a headlock as they sank into the lake, but Bond got the upper hand and then choked him out before escaping back to the surface.

Does this make any sense? As far as I know, when people get strangled they die or lose consciousness because of lack of oxygen. If you are completely submerged underwater, you dont have any access to oxygen, so what difference does it make if someone is also choking you out?

Cutting off the circulation of oxygen in the body.