No. They add a second to the year occasionally. The second was defined as 1/86400 of the average day, then redefined as a certain number of oscillations of a cesium atom, but the atomic clocks are more accurate than the original measurements for the length of day. 23 leap seconds have been added since 1972 with another one planned at the end of the year. You are correct, and this article is absolute nonsense.
But if the article was accurate, and adding a second was a big problem, just think how bad leap years would be!