Correct me if I'm wrong because it's been years since I've watched the video, but I believe Sal's method was to alternate sides between strokes. In my experience this works perfectly well for maintaining an already reasonably sharp blade.
But I always get better results doing fifteen to twenty strokes on one side, checking for a burr, then fifteen to twenty (or more depending on the knife) on the other side.
You're right, you don't have to raise a burr to get a perfectly sharp knife, but it does help to speed up the process and show you what areas you need to pay more attention to. There's nothing more annoying than a knife that is hair popping sharp, but has a half a centimeter dull as a brick spot in the middle. Raising a burr will eliminate the possibility of that happening.
I think I may go pop in the tape and watch the video again... it's been at least four years.