This is a lie. The leap second is not added because the earth is slowing. It is added because the year is not excactly 365-1/4 days long. The leap second is to compensate.
Well, yes and no. Click here for a description of leap seconds.
The last leap second, BTW, was added in January, 1999 -- three years ago. By historical standards that's pretty long.
No, leap seconds are indeed added to civil clocks to account for the lengthening of the mean solar day caused by deceleration of the Earth's rotation due to tidal braking.
The last leap second adjustment was made on Jan 1 1999.
See USNO Leap Seconds for the excruciating details.
FWIW, there is currently a proposal to forego leap second corrections altogether, and let civil clocks drift with respect to the mean solar day.