airplane-mode on the iPhone shuts off Wi-Fi, Bluetooth, ...GPS.
My understanding is that GPS-devices only /receive/ GPS signals, they don't transmit anything, so I don't understand why this needs to be shut down. [Of course, if the iPhone is running at all, then /it/ is emitting some RF, but I don't see why receiving GPS signals should cause an additional problem for the airplane.]
I tested on an iPhone 3GS (IOS 6.1.3): Enabled airplane-mode, then turned-off the phone. Rotated the phone 180-degrees. Turned it back on (with airplane-mode still enabled). The compass-app still seemed to find North.
Would someone be willing to do an independent test of this?