Actually ths statement is wrong. We had a specific descussion about the difference between friction coeff. and the area to which that coeff is applied.
the coeff. of static friction is independant, of area. YET, the total static friction IS a function of area as well as the coeff. think of the coeff as a multiplier.
A good example of this is lets say you have a tire of compound X and say its a 195 section width. Now you have that same compound in a 335 section width. The grip power of the coumpoud of rubber is the same in both tires, YET which do you think has more mechanical grip??