Some basic physics: Contact area with the ground does NOT increase with a wider tire. It just changes the shape of the contact patch. That's given the same tire pressure in the wider and narrower tires. Even car magazines make this mistake, talking about putting "more rubber on the road" with a wider tire, and therefore sticking to the road better.
(Think about putting a bicycle-width tire on your MDX, pumped up to 32 psi, which isn't much for a bike tire. What's going to happen? Assuming it doesn't explode and the wheel can take the weight, and assuming the sidewalls are high enough that it isn't sitting on the rim, the contact patch will be huge compared to the tire, just not the same shape as the regular tires.)
If wider tires did cause more rubber on the road, woudn't a dually pickup be able to do about 2 g's on the skidpad. Or a semi even better? Or a Jeep with fat off-road tires? Those vehicles are some of the worst on the road for cornering. Cars with skinny tires can pretty well keep up with wide-tired cars. (For example, put the same performance tires on an old Toyota MR2 in 185 width as a new 350Z in, say, 245 width. The Z won't be able to run away from the MR2 - in cornering. (There are some balance issues that will have an effect, and maybe roll issues, etc.)
Also, if wider (and more) tires put more rubber on the road, wouldn't the pickups and semis of the world be able to brake on a dime? And sports cars with skinny tires be terrible? And motorcycles... would the brakes even work?
At autocross events, not everybody that's competitive runs fat tires, and sticking in corners is a lot of what that event is about.
Tread compound makes a huge difference, of course, and wider tires tend to have stickier tread compounds. So there is a correlation between real-world wide tires and how well they stick.
Also, lowering pressure to acutally increase the size of the contact patch won't increase traction (on a paved road). The coefficient of friction is the same but the pressure on the road will be less per square inch of contact patch. The result is the same "stick" to the road.
Wider tires do have some advantages, in some cases, though, like less heat buildup at high speeds due to more rubber to take the heat, and they'll last longer, all else being equal and set properly. They also won't tend to "roll over" off their tread during aggressive turns as much as a skinnier tire, and this will lead to traction benefits.