If this was strictly true, you'd never blow a tire by overloading it.
However, I will agree that in practice (and at normal load ranges) your analysis is correct.
That's true... its not absolute, but for practical purposes its safe to say that additional weight won't increase pressure. But, your demonstration isn't entirely accurate.
The reason tires blow from too much weight is not because you have overloaded them and increased the pressure, its because you have added more weight than the tire can support with its rated pressure. The tire then deforms and the heat buildup from friction in the sidewall causes the tire to fail. Even if you add crazy weight without the car moving, if the tire fails its because you have deformed the tire beyond its reasonable limits.
Think about E-range truck tires. The carcass of the tire itself doesn't hold any more weight than a passenger tire, but the design of the tire is made to hold more pressure. That means the tire can use more pressure to hold its SHAPE under heavier loads. The air isn't suspending the weight as much as it is properly allowing the tire to do its job. That is why proper tire pressure is more a function of vehicle weight than the actual tire on the car. If I put the same 215/65-14 tire on my E30 and my 66 Pontiac, the proper pressure will be very different. That is why manufacturers publish tire pressures on the CAR, not the tire. Tires have a max pressure and a max weight, but its the weight of the CAR that determines proper tire pressure. Again, we technical GRM kinda people know that its not absolute, but the pressure is only there to hold the tire where it should be.
Now picture a balloon. If you inflate it to 1 psi and squeeze it until it bursts, its not that you've increased the pressure inside the balloon, its because you've deformed the latex to the point where it fails. If you put a pressure gauge on a balloon you would see that the pressure changes very little when you squeeze it.
But, like you say, its not absolute. If you add a couple tons of weight to your tires, the overall volume of the tire may decrease slightly, but for practical purposes you won't be able to tell a difference with a pressure gauge.
People think that tire pressure is what supports the weight of the vehicle. It doesn't... it simply supports the tire so that it can operate properly.