There's no evidence [NYT] that it can't crash the plane. Aviation-wonk Jim Fallows points out that pilots regularly use technology passengers are made to power off. The only defense of the regulation he can muster:
[H]ere is the only, admittedly weak rationale behind the "turn all equipment off" diktat. If anything went wrong on a crowded airline flight, the flight crew would need everyone's full attention, now. The prevailing theory is that passengers are less likely to be distracted if they're not cocooned by their acoustic headsets or distracted by their iPads.