If our clock are set to 24 hours, and the rotation of the earth is four minutes less, it would not take too many "days" for the clocks and rotation would be out of whack. For example, one week would put a a 28 minute difference!
So I am thinking that either 1) the 23 hours 56 minutes, and 4 seconds is wrong, 2) there is some automatic "leap hour" adjustment that happens when most of us are sleeping, or 3) our traditional hour is actually based on the 23, 56, & 4, which means that it is 1436/1440 of what we think an hour should be.
Otherwise an interesting article.