I maintain and synchronize railroad crossing equipment and while most of our event recorders are GPS set, the equipment that triggers the crossing isn't because we don't want any potential outside interference with those. I take my job extremely seriously, as does virtually every other signalman for every other railroad.
Many people are dumb fucks and think they can either beat a train doing 60+ mph or that 35k tons of coal stops on a dime, and they go around the crossing gates when the warning time is 20-30 seconds prior to arrival of the train at the roadway, while still taking it easy for the rough road. When they get hit, they (or more often their family) likes to think big railroad will pay out big time, and they file a lawsuit claiming our shit didn't warn them in time. However, we have proof the lights/gates were operating an appropriate amount of time before the train arrived at the crossing, and we counter sue the insurance company and/or dumbass for costs of damages to our locomotive(s) and cars, crossing equipment, injuries to our own personnel, etc. If I'm not checking/resetting the euipment for computer processor timekeeping inaccuracies, they may just get out of paying for their own stupidity along with getting people like me fired for not doing their job right when we thought we were, all because of a watch that keeps shit time.
So yes, to the second accuracy matters for more than the military or simply being somewhere on time, and I'm just one small field of work amongst many that require the same kind of accuracy in timekeeping. We don't work to split seconds, but we do need the equipment to match each other when it goes in front of judge and jury.
I worked with one gear queer who had a Rolex he would wear to work, and I would fuck with him incessantly when he would break out his phone or ask me what time it was when setting clocks. It's like bringing an F-Class rifle to the Steel Safari, what's the point if it doesn't work?