No, I think the actual pressure inside the tire is the same, no matter where you measure it, top or bottom . . . . although, tires do seem to always go flat *only* at the bottom
The thickness of the tire carcass also throws the calculation out of whack - The area of the contact patch (the air supporting the load) is different inside the tire from what you measure on the outside where the tire contacts the road surface due to the thickness of the tire
As I said, your 'theory' is correct, but the tire throws off the accuracy of the calculation and because of that, you always get an erroneous answer
Don