There are many ways to bind off, but I think most people just use chain (plain old) b/o in pattern for most things. It really depends on what look you want to achieve, and whether you have special situations, e.g., you might want an extra stretchy b/o for socks to make sure they will clear your heel when you're putting them on.
The video you're referring to makes a nice looking b/o for single rib. If you like the way it looks, try it out on your next project. It can be tricky at first, but if you're familiar with kitchener (grafting), it should be familiar to you, because it's basically the same, except that everything is on one needle instead of two. (You can actually separate the knits and purls onto two parallel needles and do it exactly like kitchener if it's easier for you.) Other names for the same b/o are kitchener (no surprise!), tubular (because it's often used to b/o tubular knitting, aka double knitting), and invisible (because the stitches seem to wrap around the edge and go up the other side as if there weren't bound off at all).
There is no right way to knit; there is no wrong way to knit. So if anybody kindly tells you that what you are doing is "wrong," don't take umbrage; they mean well. Smile submissively, and listen, keeping your disagreement on an entirely mental level. They may be right, in this particular case, and even if not, they may drop off pieces of information which will come in very handy if you file them away carefully in your brain for future reference.