Think for a moment about a standard balloon. If we increase the inflation pressure, the balloon does not become a square. In fact if we placed the balloon on a table and hold it down with our hand and then increased the pressure we would seen the side bulge out and be more curved. A tire section as seen in this picture (by Pirelli) is much like the cross section of our balloon held between the table (this case the rim) and our hand (the belts). Increasing the pressure will not make the sidewall go straight but in fact when measured will make the width increase due to more curvature. If we check Wikipedia for "Contact Patch" we find "The larger the inflation pressure, the smaller the contact patch".
I will leave you with some additional pictures. You can see how under-inflation will cause the shoulders to wear while over-inflation will cause the center to wear faster.
Here we see the results of a simple test where a chalk line is drawn on the tread. With an over-inflated and then under-inflated condition the tire is driven a few feet. It is easily seen that the center of the tread is supporting the load in the higher pressure (overloaded) condition.
I hope this answer Gene's questions.