No, this is the point of the article. The person without the seconds could not tell if you were late or not when his watch says 1:00. A display of 1:00 means the actual time is between 12:59:30 and 1:00:30, so there's a 50% chance the person arrived early. Only the person with the second hand could tell for sure.
It's a bad point. If the clock says 1:00 and you aren't there you're late.
Your boss won't like hearing "well technically I wasn't late because you see your clock has the seconds rounded to minutes so you can't actually know if I'm late".
The best possible outcome you could get from that is that the meeting starts at 12:59:30 now.
I'm simply communicating the point of the article. Take it up with the author if you don't like it or don't agree. And he'll tell you that if sub-minute precision is necessary (i.e. someone would be reprimanded for being under 30 seconds late to a meeting) the simple solution is to include a second hand on those clocks, and there won't be any confusion. (Of course, what's the likelihood of a basic office wall clock being accurate to within 30 seconds anyway, but that's a whole other rabbit hole)
This is a weirdly satisfying thought, if entirely unrealistic in a corporate setting: what if meetings in general were more of a consensus thing, and less of a rigid time slot thing.
