Any cast on would be correct on any garment in my opinion, most definitely.
However, there are lots of cast ons and bind offs out there and people are always trying to create new ones because each one has its own benefits that you may or may not want in a project.
For example, I made a pair of mittens for a friend of mine and I used Ysolda Teague's tutorial on invisible tubular cast ons to give it an edge that, for the most part, could not be differentiated from the body of the ribbing as well as being very flexible. This gave it a more "finished" look but is no more "correct" than if I had used a long tail cast on.
This has become my regular cast on for most things with ribbing as its reasonably easy for me to do and is really stretchy. But I definitely still wear all the things I made before I started using this cast on.
Likewise, for the project I'm doing now, I want a decorative edging for the bracelet as both edges will be in constant view from different sides. So I want both edges to match and be as finished looking as the tubular cast ons and bind offs are for 1x1 and 2x2 ribbing. But I certainly don't need them to be that way.
I just wish I knew someone who has done this Channel Island bind off because I will end up ordering this book if the library can't get it for me.