The video shows that the measurement phase lightly touches the string. During grinding, the strings are pulled off to the side. I don't think strings are damaged during the process. The height of the fret is determined by it's distance from the string. The frets are ground down as necessary to make the distance from the top of the fret to the bottom of the string to be the same.
Seeing as how I have seen the process repeated approx. 15 times a day 5 days a week since October of 08, I can assure you that bass strings are not affected. If the strings were affected this would surely affect the marketability of the device. Now it's a possibility that lighter gauge guitar strings (think .07) could be affected when the instrument is tuned to pitch. I am not certain seeing as how I have only seen 1 strat plek'ed.