Has there ever been a proven case of interference with aircraft systems from a passenger carried device? References please.
Last i read on this, there was a reported case of laptop interference in some 757 and Boeing even sent up the plane afterwards, empty of course, with the laptop to see if they could reproduce it, and couldn't.
I have been developing electronic products since the 1970s, hardware and software. Much of the stuff written above about susceptibility to EMI is nonsense; if it wasn't there would be transport planes crashing everywhere because there will always be a few people leaving their phones on.
Having a no-gadget policy is fine as a policy but claiming it has a proven technical basis is bogus.