With Mandarin having now been confirmed this may sound like non-news about The Ten Rings in IM3
but it does seem it's going to retroactively confirm their involvement in Iron Man 2 with Whiplash most likely.
In Iron Man 2, a scene was cut (or not filmed) where a man who gave Whiplash fake documentation revealed himself to be an agent of The Ten Rings (this remains in the novelization from what I’m told). Jon Favreau had a great scheme he occasionally mentions to reveal at some point in the Iron Man film future that The Mandarin was behind many of the Stark family’s struggles.
Looks like that vision is going to continue if the Iron Man 3 crew hat is any indication of logo fidelity.
The hat is pictured in the link. Along with the original reference from IM1 for the hat's logo design.