The tire labeled MAX pressure is the most it should ever have in it. The door jamb is only for OEM tires the vehicle came with, not the next generation of tires which are made for different pressures. So the maximum is on the tire, and the OEM suggested amount should be used as the minimum pressure.
Remember that OEM were half at fault for all Firestone tire failures of the old gen trucks. The tires had a defect, but running the low pressure listed on the door jamb just created more heat, and on trips it caused failures. I was on an 1100 mile trip back then when the recall was announced. I had the Firestone's on my 93 truck, and I had no trouble, I got another 15k miles out of them. I had about 32-35psi in those tires, which was the ideal amount for my stock vehicle with the stock type tires. The door jamb is a bad place to get tire pressures from, unless it's brand new.
The subject is large but 90% of the debate is always each individual person's ignorant belief of some magic random pressure they claim works for all tires, or their car, or what the dealer told them etc.
The best pressure varies by the vehicle, the weight of each end, the tires used, the usage, and the driver's habits. There is no one pressure that is right for all. The best answer is tire wear, use what is needed to optimize the wear.
I put more in the front because that end is heavier and needs more air to even the tire wear, and I don't drive 90% highway at 55mph. I use the same pressures in the next set if they are the same exact tire. If not, I start over again and watch tire wear carefully, starting with pressures I find worked best before, and adjust as needed. When the centers wear faster, reduce the pressure, when the edges do, raise it. It is that simple, begin with a figure several PSI below the MAX pressure, more in front, less in rear, and drive it. Check the tires often, at 1000 miles you shouldn't notice any odd wear, nor at 4-5000, But it you do, when you do, adjust them carefully and rotate, and keep watching them. Once you learn what they need, that specific set of tires, you can continue with those pressures until the next time you change tire brands or type etc.
My 98 with Cooper likes about 37psi in front, and 34psi in the rear tires, the MAX being 44psi.
