the pliable stuff is lycra binding I believe. I used some to make some straps, and yes you can bend it around the curves pretty well. The rigged stuff that's on the ULA Ohm I have is just grosgrain, and the Golite Ion I have on hand is just some type of nylon webbing. The ULA doesn't actually go around the bottom curve of the strap, but the Ion does, I imagine they used a binding inserter to make the look good.
The advantage of the lycra binding is that you can stretch it around the curves, just make sure you get your stitches even along the edges of the straps and then cut the lycra 1/8th inch from the stitch line. It doesn't unravel. The disadvantage is that it's kind of a PITA to get it tightly wrapped around the main strap material.