You need the right balance of air pressure. Both too much and too little can reduce comfort.
This can be seen by thinking about the limiting cases. With no air, you're directly on the ground. If you could put very high pressure into the mattress without it exploding, the mattress would itself be hard, and you're effectively back to being on hard ground.
You want something in the middle. The best for distributing your weight over the most body area is when the lowest point on you body just touches the ground. That is usually the hip when lying on your side. With the hip not quite touching the ground, you don't feel the hard ground, but the mattress is selectively squished and conforms to your body up to the depth of the mattress.
I've got one of those inflatable pads that's maybe 1 inch or a little more thick, and I have found the above works just like the theory suggests. I usually over-inflate the mattress when setting up the tent, then let a little air out when I lie down. I do this while lying on my side since my hip in that position is the first thing that touches the ground when the mattress is under-inflated.