That may be true with newer AC and phones, but it wasn't always the case. Many years ago (early to mid 90's maybe), I brought two mobile phones (Audiovox bag and Motorola MicroTac) with encryption gear on board companies new glass cockpit G IV to determine feasibility of encrypting execs communications after the company lost a couple of large lucrative contracts. Corporate chief pilot gave me a quick tour and powered her up.
He had already told me that on just about every flight they were getting random and frequent display messages forcing the crew to instruct Pax to turn off all electronic devices - mostly laptops. Spent quite some time on board (the G IV and two other AC) making calls with both phones and moving around the cabin. Location didn't seem to make a difference but both the 3W and .6W phones caused the messages to start scrolling. Not surprisingly the 3W phones generated a larger number of alerts but both ultimately did the job. It was always an added burden on the crew to determine what was real and what wasn't particularly since glass cockpits were realtively new to them - a distraction at least that could occur at times when the crew really didn't need to be distracted.
I realize that RF emmissions have changed and shielding has gotten much better, but I always turned my phone off after that and it annoyed me when I saw people leaving them on. It still annoys me today simply from the perspective of not following crew instructions.