"It will have the same contact patch as the thinner wheel/tire...as long as the weight is the same."
exactly, this is why tire sizing(width) is less important than compound for grip. Take for example the acura NSX, an excellent handling car by any measure, ran a 225-50-16 rear tire. Not 'wide' by any strech of the imagination, yet still turned a nice .96g on the skidpad and a great slalom(sp?) speed.
what you really do with a wider tire is make the contact patch wider, instead of longer...which CAN help. It makes the tire itself a bit better at resisting lateral forces(think wide versus narrow stance), and since the contact patch is wider, it makes a higher percentage contact with road...
I'll explain:
think of a gap in the road surface, typically these run perpendiculat to the tires contact patch. in a narro tire, with a long contact patch, the gap in the road surface would take up more(percentage wise) of its contact patch than a wider tire. make sense?
so wider tires do provide some benifit, to a point. Wider tires usually come in stickier compounds, too. The compound and tread design has more to do with tire grip than the size.
hope that helps!also, just FYI the engineer behind the new 350Z chose its tire sizes because the patch would be longer than it was wide, for the vehicles dynamics work better with it that way

-chet