I just saw the video of the knife slashing through paper quickly, couldn't tell much from it.
I don't think a blade needs to whittle hair - at least not if you use it often. Depending on which knife it is, how I use it, what I use it for, every knife has a different edge with a different level of finish. I use my finger nail, visually observing the edge, and paper to test all of them though. My main concern is that everything is consistent - if I only put a 600-800 grit edge on it, I want the whole edge to have the same finish, be a consistent width, and be free of burrs. Slide your finger nail along a blade that has been used heavily - it will be rough in spots. Now slide it along a good blade that is freshly sharpened - it will be very smooth. Now that you see where the rough spots on a blade are, cut the paper slowly drawing the blade through the paper. You will feel those same rough spots on the paper. If the blade is long you may have to make as many as 3 cuts to check the entire edge.
In my experience, this is about the extent of what printing paper will tell you. I have handled very few knives that will not cut paper (excluding knives that have been worn out from cutting or extremely cheap steels), but I often cut paper to check blade performance. Like other people said; if the knife is performing to your expectations, it is sharp enough, but a lot of people try and push that to its limit. It isn't always necessary to spend 3 hours sharpening knives though - a toothy edge will cut some material just as good as a refined polished edge, and at the end of the day the knives can be in the same shape (the refined edge will degrade much faster). It gets to a point where there are diminishing returns, at least if you are using the knife daily.