I read a review in a computer magzine (cannot remmmber which, maybe PCA) a couple of months ago. The product was highly regarded. So their claim maybe correct.
But you have to put this is context. For downloading files, this cannot happen technically because almost all files for downloading (zip, mp3, Rar etc) are already compressed, so cannot compress further.
The main thing can be compressed is text file which is want web page use. So if you just use web for site broswering and download email, the speed increase is difinitely possible by compressing (this is every speeding such as onspeed do). For graphics, most web pictures are in ipg format which is a compressed format cannot be further compressed without loss of quality. All speeding programs can speed up web suring with pictures by reducing pictures quality.
One thing to consider, all web traffic will go through their server, so security issues may arise. I think some shopping site may not allow you to carry out transcation through this method.
I only guess (based on technical possiblity) because I have not used this service.