Actually, that video clip demonstrates that the best solution to avoid a crash is not tires, brakes, or anything other than making sure you have an 'escape lane' and clear blind spots at all times.
I took a defensive driving class at 16, and the number one thing they taught us was to always have an open lane to swerve into if you need to, which is exactly what happens in that video. Blocked lane ahead, swerve two lanes over.
If I get boxed in by cars, I always brake until I have room to change lanes in case of an emergency. Although, grippy tires help with high speed swerving lane changes