The Kinect only relies on Prime Sense in the form of their hardware. All the algorithms and software are entirely developed by MS Research. This point is made more clear by the fact that Microsoft didn't acquire exclusive rights from Prime Sense but is instead banking on the superiority of their algorithms.

I've played around with the Kinect, and without Microsoft's code, all you really get from the hardware is a depth image (think an RGB image with distance from camera for each pixel instead of intensity). Everything else is developed by Microsoft, and it is not an easy feat.

Prime Sense developed their own software for pose detection and tracking, but it is inferior to the XBox360 implementation.