I think it is a non-issue. For most of the 80s and 90s I carried an 800mz Motorola PT (the first "blackberry" type device) and originally they had dire warnings about using them in the computer room. Of course we still did. After a few years they decided they had never found a case where it bothered anything, even when we were actually under the covers.
These things were a lot more powerful than a cell phone or key fob (5 watts) They were also listed as being "intrinsically safe" for you classified location fans.
This is the same BS that they spread about cell phones crashing airliners and blowing up gas pumps.