Fall Colours socks V: tubular bind-off for k2p2 ribbing

Because these socks have no heel—one simply goes on knitting, changing colours on a whim, until reaching the desired length—there is not much to add pattern wise. There is, however, a choice at the end: no cuff, just continue working in spiral ribbing to the end, or a k2p2 cuff, done by stopping the spiral and working in plain rib for one inch or so. After that, we need to bind-off and for best results we will work a tubular bind-off.

I have been having trouble finding a good tutorial for this technique. The ones I have found do the following:

1. First, in one round, redistribute the stitches in such a way as to obtain a k1p1 rib. You can use a cable needle to help avoiding dropped stitches. What you do is crossing the second knit stitch in front of the first purl one.
   
   
2. Then work the normal tubular bind-off.

However, there is a way to avoid redistributing the stitches and work the tubular bind-off directly. I found it in Montse Stanley's book and after going through a lot of video tutorials I finally found one that shows this technique:

There is however a difference between the instructions of this video and those of Montse Stanley's book (a mistake? in any case, it does not seem to make much difference). This is the following, after the set-up stitches, when working the two purl stitches, Montse recommends going around the back of the knit stitch (note there is only one left on the needle).