As was already posted, it is counter-intuitive.
If you are in a circular orbit, and fire a thruster to increase your forward speed, you are going to go into an elliptical orbit with the highest point being above the original circular orbit, and the lowest point being the same as the circular orbit. When in the new elliptical orbit, you will be going faster than the circular orbit at the low point, but slower at the high point, because you have gone "up" in altitude with what was the "extra" velocity.
And, when at the high point of the elliptical orbit, you will be going slower than the speed needed for a new circular orbit at that new high point. So, if you fire your thruster to get more forward speed while at the high point, you end up raising the low point. If you do it just enough, you end up with a new circular orbit at the altitude of the high point of the elliptical orbit.
Getting back to whether the article is stating things correctly, yes it does. The "drag" from the thin atmosphere at the ISS altitude does slow it down. The orbital dynamics then cause it to drop its low point, where it will be faster than it was at its high point. The opposite of what I described above. But, because drag is a continuous process, rather than a discrete impulse, the resulting orbit is a spiral, not an ellipse. It still stays close to circular, because the drag is slight compared to its total momentum.