I never believed that mobiles could affect an aircraft either and always assumed that it was just because of the overlapping cells from altitude thing, until the following (true) story

I flew up from London to Birmingham in a small aircraft a few years back. I was piloting the aircraft. The flight up was uneventful and the weather was beautifully clear. On the way back was a different story, cloudbase starting at about 1500ft in the local area, but clear further down south.

On the way back as usual I'd asked the passengers to make sure they had their mobiles switched off before we started off, and I took off and headed both down towards Coventry and up into the cloud. I was navigating using the VOR (for those that don't know, this picks up a signal from a groundstation, and tells you what bearing to fly towards (or away) from the groundstation, it displays in the cockpit as an instrument with a needle in it, you set the bearing you want to fly to/from the groundstation, and fly, making course corrections as necessary, the aim being to keep the needle in the middle which would mean you are on course).

The point was things weren't quite right. You develop a good sense of spatial awareness when you fly on instruments and you end up keeping a 3-D model in your head of where you are, even if you can't see a thing out of the windows. We were having to chase the needle too much, and the course we ended up following to keep the VOR needle centred just didn't make sense. As best I could work out (which isn't easy in cloud) we were flying around in circles

Without alarming the passengers I put us into a holding pattern to try and work out what was wrong, and was trying everything, switching on/off the VOR, calling the ground ect. I was just about to call a PAN (a request for assistance one level below a MAYDAY) since at that point we had been circling somewhere above Coventry for about 20 minutes with no real way of guiding us, and a big question mark as to whether the VOR was even working at all (which would have meant abandoning the flight). For some reason I turned my headphones up full, and just heard the faint sound that you get if a mobile is held too close to a radio or music system. Quizing the passengers one checked in his bag and found, yes, a switched on mobile. He switched it off and the VOR jumped back into life immeadiatelly, this time pointing the right way, and we were able to safely continue the flight.

As I said, I never used to believe it either, but (at least in this case) they really can interfere with the aircrafts navigation systems.