Tires are a somewhat special case in the frictional force world. Here is an interesting article that explains why a wider tire (and therefore surface area) is better for stopping:
The basic premise is that the tire road surface is not an idealized coefficient situation. The tire has the ability to shear at the contact point with the road and therefore the wider the tire the more shear resistance is available.
There are also deformation issues based on road conditions. If the road was extremely flat and the tire shear issue was solved then surface area wouldn't affect the situation as much (or at all).