Let's assume a 200 pound rider and bike unit. Let's also assume that the weight is distributed half over each wheel. That means that each wheel is supporting 100 pounds. Now, with a pressure of 100 pounds per square inch, the contact patch is one square inch. This is true no matter how fat the tire.
I dont' think this is true. Just looking at my wheels while off the bike, a lot longer than one inch is touching the ground. That length will be the same for every tire of the same diameter. Multiply that length by the width of the tire actually touching the ground and you get the contact area for an unloaded bike. When you put your weight on it, that area is going to increase a little, but probably not by much. So a wider tire of the same diameter and pressure will have a larger contact area.
The ride quality may be better for the wider tire, and that's really all that matters.