EMI from electronic devices do affect navigational systems. If you want a demo of this in your house, put your iPad next to a magnetic compass and watch it swing.
In the little Cessna that I fly, my portable GPS will cause the compass to be off by as much as 3-4 degrees.
I know this is much different than commercial jetliners -- I don't claim to know how commercial jet navigational systems are built. I do know that most of the FAA regulations (such as turning off portable electronic devices) are typically created from incidents that have happened in the past.