I have no doubt a single hot lap would be fast with the supercharger. But that's not really possible as nobody does just one lap sessions and tires wouldn't be heated enough to provide adequate grip for faster times. You can say I had bad corners all day long but I'm the one who put a decent amount of track and street time with and without the kit and the numbers just go along with what I already felt since day one.
Of course I'd love to see a professional driver independently compare them as well. But my conclusion is based on my own data and experience and I'd say that's at least better than theories and vendor claims. You should buy my kit and test yourself.