Let's see, how many dangerous modern electrical toys can we combine into one stunt? These guys at the 2012 Western Winter Teslathon enclosed a quadrotor (or quadrocopter) in a Faraday cage and flew it between two Tesla coils for a electrifying light show. See another video from the same night at Laughing Squid. Link
And Ray's answer is probably the right hint---maybe the cage spacing determines which frequencies it's permeable to. So, it's impermeable to whatever fields the Tesla coils put out. But the RF from the controller gets through. (I'm surprised that there still isn't an interference problem, though.)