The road may or may not be the culprit, but it certainly CAN be the culprit. Wider tires have much more of a tendency to hunt and dart around the road, and braking just makes it worse often times.
If it's slightly uneven pavement, or let's just say the car's on a slight lean due to the road, braking will exaggerate the effects and cause the car to pull more to the lower side.
Please correct me if I'm wrong...
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