The issue isn't that interference can't be caused in cruise (it can), but that takeoff and landing are more critical times. PED interference is documented; it happens. I've experienced it once that I'm aware of, although like most cases of PED interference, I cannot without question state that it was a personal electronic device. The situation couldn't be duplicated, and I could find no other explaination.
If you review the ASRS data base, you'll find several hundred reports detailing control and navigational problems that have been attributed to PED interference. While it's logical to conclude that a certain number of those reports may be crews trying to pawn off a mistake on a catch-all problem, I believe that many such reports are indeed genuine.
While at first blush a small electronic device may not seem like much, one has to appreciate that it's being operated in an environment which can amplify or alter the signal or signal byproduct, and which places wire bundles and devices, antenna coax, and a variety of potential receptors. Any electronic device outputs electromagnetic fields and electromagnetic radiation in a range of frequencies. One of the harmonics for a generic CD player, for example, coincides with VHF nav signals, and can cause interference with VOR and ILS reception. The interior or the aircraft tends to reflect this signal, and there is always a potential for interference.
The topic is hotly debated, but that doesn't change the fact that numerous cases continue to be reported of PED interference with flight control and navigation. Most commonly navigation.
I'll restrict my comments here to generic terms. I'm not an electrical engineer, nor an avionics tech. I know that some folks who read this board are engineers and have avionics backgrounds. For them, I say please ignore my simplistic view and potential misuse of terminology. The sole point of my comments is that PED interference is a genuine concern, or should be.
The potential for interference enroute is the same as departure or arrival. However, the risks are potentially higher in the terminal environment, or close to the ground.
Since Avbug mentioned engineers, I'll follow up - my graduate work was mostly in electrical engineering and nuclear physics, and I have about ten years OJT between my military and civilian flying days - and with all that, I couldn't have said it better than Avbug. Everything he said was dead on.
Here's a few other little bits -
A couple of years back, they actually conducted tests using cell phones in several parked jet liners - the cell phone signals were detectable in the cockpit from every location on every plane tested except for the aft baggage compartment and aft galley of a B747 (although, surprising to most people, it's actually the FCC that bans cell phones in flight - because of switching problems).
All modern digital electronics have some form of frequency generator - even small radios; certainly CD players, portable GPS units, cell phones, and Palm Pilots and laptops; even beepers. They all have some sort of oscillator to generate reference signals and/or allow digital processing. It's that frequency generation that causes the undesireable "signals". The only device that may not have a frequency generator is an older tape player.
And the other contributor is the long wiring runs. Those wires that run the length of the airplane act like antennae, and if their length is right they can actually resonate with a signal. If you have a "T" wire antenna for your stereo you'll notice it's just over three feet long. They're actually normally one meter long, which makes their length exactly equal to the average wavelength of an FM signal - so the antenna will resonate and pick up the most signal possible. The aircraft's wires can unintentionally do the same thing.
Finally, as Avbug said, the mechanism by which PEDs interfere with aircraft equipment still isn't generally known; different devices have different effects on different equipment, and actually most have no known specific effect, even though they may be generating detectable interference signals. It's as much these unknown aspects that make it a good idea to turn them all off during the critical phases of flight, such as T/O and LDG. Up at altitude, the fall out of interference is minimal; but the last thing we want on a CAT III approach is for something to mess up the autopilots or ILS signals.