I know what you are trying to get at, this is why I said we are all splitting hairs.
You want me to reply that the tire could dig in because of too much traction. But, lets remember....you said puney tires will push rather than gain traction.

Puney, high profile, non-performance oriented tires can be stressed beyond their intention, roll over onto the sidewall (and possibly off the bead) thus suddenly increasing the contact patch and then....due in part to an instant gain in traction, and a suspension not engineered for these sudden and excessive loads, could cause a car to roll-over, especially if the vehicle has a higher center of gravity.
So yes, a sudden gain in traction has much to do with a car's tendency to roll over. But, has more to do with several factors combined like suspension geometry pushed beyond it's limit, a higher CG, and tires not designed with high performance characteristics. Any number of these ingredients combined could easily lead to a roll-over, not just "too much traction."

Throw in a dose of over-enthusiastic driving and a very technical and tight auto-x course and you could have a reciepe that could lead to (although rare) a vehicle roll-over.

So, I'm not missing the point, I'm just seeing more of them.