I guess that's all they're doing. I wasn't quite sure if I had it right and I didn't want to go off spouting nonsense. :-)
So I guess what you do is at the start of each frame, store the verlet's position in CURRENTFRAME, and then at the end of each frame, store CURRENTFRAME in LASTFRAME. Then each frame you take CURRENTFRAME-LASTFRAME and that tells you the difference between the verlet's position between where it was and where it now is. And that tells you it's position and velocity. And because the two are combined in this way it's very difficult for position and velocity to get out of synch with one another.
So I guess what you do is at the start of each frame, store the verlet's position in CURRENTFRAME, and then at the end of each frame, store CURRENTFRAME in LASTFRAME. Then each frame you take CURRENTFRAME-LASTFRAME and that tells you the difference between the verlet's position between where it was and where it now is. And that tells you it's position and velocity. And because the two are combined in this way it's very difficult for position and velocity to get out of synch with one another.