Earlier quoted context omitted.
But then pressure (force) on each tire is lower now, so the friction is also lower. Effective friction is a function of weight and coefficient of friction between the materials. Interestingly the surface area of the contact is not part of the equation. On a flat surface a truck and a car using the same tire compound should have identical stopping distances. The issue comes when you are going downhill.
That equation works for friction between idealized solids. Tires are not even close to an idealized solid, they deform as more weight is added to them, so the contact surface area increases as more pressure is added. That is why you see racing cars with big fat tires, because it's more grip and the relationship is not linear.
The explanation in fact relies on deformable surfaces. If you imagine keeping the normal force constant and reducing the apparent contact area, the pressure on the surfaces will be increased which will cause the surfaces to deform more, resulting in more microscopic points of adhesion.