The only 2 color binding I'm familiar with is the faux flange. You stitch in the ditch on the seam between the flange & the binding so it can't shift. You are obviously talking about something different...
OK. Googled it. Yes I can see how the binding may twist a bit through laundering & use. I think you are right, the only way to stabilize it would be with an additional row of stitching.