That’s only true if the man with one watch has an atomic clock radio receiver on his watch, and furthermore if his counterpart lacks said device. Of course, we can’t say with any certainty that the signals are functioning correctly, that the watch is set for the proper time zone, etc. Measurement of time, however, is a man-made law, an absolute that inherently carries no moral force if it is not obeyed (although it would be horribly inconvenient to fail to keep time with everyone else).
-ACEGC