Ok, I watched that section again, I've got it now. (I've been watching these videos here at work and missed that part.)
Some of you guys will remember Lewis Quarles, years ago he gave a demo at a Maryland trap convention. That was the first time that I'd ever watched someone set a land snare. Lewis was using 11 gauge tie wire, and he made it a point to make sure the wire would "bite" into the tree or saplings bark. Whatever you're using for a support, twist it up tight with your pliers, make it really cut in.
For the actual part of his support wire that was holding the snare in place, he'd just make a little kink in the wire and crimp it down tight on the snare, just above or oustide of the lock.
I've never used tubing or the twist on things. I kind of like the way that Newt showed me, with 2 strands of twisted 14 gauge wire, and an "S" loop. I'll take my snips/side-cutters, and make the "S" just as small and as tight as I can. With small cable like 5/64th's, it'll kink your snare wire, but it does hang on very tight.