yellowdog's suggestion is a good one. Just don't let them feed you the "talk to your dealer" statement if you've already gone that path.

I've been thinking about this discussion, and the only thing I can come up with is that the tire's inflation pressure is roughly the same as the pressure the machine is exerting on the ground. If you do the calculation (and assuming it's accurate enough), suppose you have 2,000 pounds per wheel. For a tire filled to 40 psi, this means a contact area of 50 square inches. If you then take the weight and divide by the area, you get 40 psi. This isn't just magic with these numbers (I chose them to work out evenly), but the machine weight actually cancels out entirely, leaving just the tire inflation pressure.

If some of the assumptions hold up, this means that whatever pressure is in your tires is the pressure against the ground that tire exerts.

The reason I'm struggling with this is that I don't understand what happens if the machine is balanced, say, 90% of weight on two wheels and 10% on the other two. Or, put another way, if you pump up your car tires to 35 psi when the car is on the ground and then you lift the car in the air, what would your pressure gauge read?