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SO... Mr Smart guy. If he does switch direction on that one tire... will the BCM malfunction because of 3 tires rotating in the proper orientation and 1 being out of proper orientation? The question for you is WHAT code will pop up if the above scenario happens to cause a code to be thrown. Huh...bet you don't know that Mr Nuclear Power Plant Electromagnetic head.
I don't know about for car tires, but motorcycle tires are directional because of the way the plies are wrapped in constructing the tire - they are directional for braking purposes, not for traction or for shedding water. And some tires meant for the rear are mounted in reverse if used in another application as front tires on other bikes, so the rotational force during braking does not separate the tread from the body of the tire. Other bike tires are non-directional.
I was never aware that tires for the C5 were directional but I learned that today and confirmed it after looking it up, but that is for traction and prevention of hydroplaning (shedding water), not for braking.
Based on what the OP posted in another thread, I believe he was doing this temporarily, to try and diagnose a problem with the car "pulling" under acceleration.