Not quite. Or, at least, perhaps not.
It's possible that the 360, by virtue of having relatively equal market share, kept Blu-Ray from being a legitimate factor. What if the 360 had launched with a Blu-Ray drive? Can we say for sure that there would not have been improvements across the board? I'm not sure, to be honest, though I bet that cut-scene quality would have gone up.
On the other hand, if Sony had licensed a version of Kinect for the PS4, would it really make a big different in terms of game quality? Personally, I don't think so.
The Fighter Within would be a multi-plat game, sure, but that hardly helps the case for universal Kinect.