Killian using the Ten Rings logo in his messages doesn't mean anything. Hell, I COULD send a message to someone I know with Ten Rings logo, and that doesn't make me the Mandarin.
The stinger is that the Ten Rings held Stark prisoner in a cave for several months, and Killian did nothing. Didn't kill Stark out vengeance or even ask for help to deal with the Extremis problem. The entire Mandarin is a fake feels like something that was created very recently.