The computer vision aspects to the Kinect (and there are a lot, and very well done), were headed up by Andrew Blake at MS Research Cambridge, who's one of the foremost vision scientists in the world.

http://research.microsoft.com/en-us/um/people/ablake/

Most recently they have built the machine learning technology inside the Xbox Kinect human motion tracking system.

It is true. Microsoft bought from PrimeSense the IR depth sensor technology, but all the body recognition/tracking software was developed by Microsoft Research.

I don't know specifics about Kinect, but I do know that MSR has done a ton of work on computer vision and its applications over the last ten or fifteen years, and I would be extremely surprised if that work didn't inform the efforts of whoever did invent Kinect.