If I understand it correctly, rolling the cover would result in the clean interior layer becoming dirty due to being in contact with the exterior layer.
Possibly. I'm a driver, not a polisher

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I do like that line - i am a driver not a polisher.
This is starting to sound like the "wash your car from the bottom up or top down" thread. I will never be able to fold my one without being in a state of fear I got it wrong now.