Nike Free was promoted as a tech on the Kobe IIs, but the way it was executed on that shoe was more for show/marketing than anything else. I've owned a good number of IIs, and that shoe doesn't have nearly the level of flexibility you'd need to take full advantage of Free tech like you would in most Nike Free shoes. If you look at advertisements for a lot of Free shoes, they even market the added level of flexibility you get from Free by literally showing you how you can bend some of the Free shoes almost into a ball, which you clearly can't do with the IIs. If you have a midfoot shank that's designed to give added stability so you avoid pronating too much when you're moving around, you're obviously going to have decreased flexibility. The shank on the IIs is a major reason why Nike Free on that model was basically negligible.
The X's design is much more true to how a usual Nike Free shoe behaves compared to the IIs specifically because, like you said, they're using that carbon fiber clip on the outrigger to give added stability instead of the typical midfoot shank that you see on most basketball shoes. Because of that move, the Xs have more added flexibility and can behave more like a typical Free shoe.