Boeing has an explanation of the rationale and the steps they've taken to examine the effects of electronics on aircraft in their "Aero" magazine. This is pretty old (2000) and would certainly benefit from an update, but they did real live technical investigation instead of just mixing assertions with quasi-technical arguments. A link to the full text:
http://www.boeing.com/commercial/aeromagazine/aero_10/interfere_textonly.html
TLDR Summary:
After receiving very specific, detailed claims/complaints from airlines, Boeing inspected the frequency range output and dB level of electromagnetic emissions from several specific devices. Their biggest concerns in the testing seemed to be the EMI due to frequency harmonics and interactions between devices--the premise and conceptual explanation seems unlikely but isn't completely meritless. No airplane susceptibility was demonstrated. Boeing clearly said that since they tested specific items, the testing was not conclusive for all devices and all interactions.
The excerpt on cell phones in particular deserves to be fully quoted, as it illustrates their thinking:
*Cell phone tests and analysis.*
Boeing conducted a laboratory and airplane test with 16 cell phones typical of those carried by passengers, to determine the emission characteristics of these intentionally transmitting PEDs. The laboratory results indicated that the phones not only produce emissions at the operating frequency, but also produce other emissions that fall within airplane communication/navigation frequency bands (automatic direction finder, high frequency, very high frequency [VHF] omni range/locator, and VHF communications and instrument landing system [ILS]). Emissions at the operating frequency were as high as 60 dB over the airplane equipment emission limits, but the other emissions were generally within airplane equipment emission limits. One concern about these other emissions from cell phones is that they may interfere with the operation of an airplane communication or navigation system if the levels are high enough.
Boeing also performed an airplane test on the ground with the same 16 phones. The airplane was placed in a flight mode and the flight deck instruments, control surfaces, and communication/navigation systems were monitored. No susceptibility was observed.
Telephones installed and certified on the airplane by Boeing or operators are not actually cell phones, but part of an airborne certified satellite system. These phones are electromagnetically compatible with the airplane systems because their emissions are controlled. In contrast, the emissions from passengers’ cell phones are not known or controlled in the same way as permanently installed equipment.