Why then do they not have people remove the batteries from their watches? Can't they also be unintentional radiators?
what spa942 said.
From the linked thread:
"The low power in a digital watch is certainly a factor but the main thing that keeps them from interfering is very low operating frequency. In older, simpler watches this was 32 kHz! Only one octave above the audible range. In more modern multifunction watches with stopwatches that go to 0.01 seconds (as if anyone can push a button that precisely, but never mind that) they do have to be clocked faster, but they are still clocked as slowly as possible, to save power.... typically 1 MHz or less.
The RF from these things is all but undetectable unless you put a pickup directly against the watch. "