I seriously doubt there is $15K worth of additional stiffness in those carbon wheels!
The real benefit is the weight. The test Porsche has certainly had the suspension rebound and damping set for the lighter unsprung weight of the carbon wheels. You throw on the heavier aluminum wheels and everything will be off! The wheels won't follow the undulations of the track quite right, and you'll get the impression of less grip.
I did a track day once on my motorcycle at Buttonwillow. I thought everything felt pretty good with the factory suspension settings, but then I had a guy tune my rebound and damping right there at the track. The difference was amazing! The bike just felt planted like never before, even on off-camber turns.
I think this is the real difference Jay is feeling in the seat of his pants. You can't really feel the 1 mm of flex you'd get in a factory Porsche wheel.