Digital camera connection

I am getting acquainted with my first digital camera, a Fujifilm DX-10. The owner's manual warns that both the computer and the camera must be OFF before they are connected. I can understand this for the camera, but if the camera is Off what damage to the data or the hardware might occur if the the computer is ON when the cable is plugged into the camera? I never disconnect the cable at the computer end.
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When you play with fire there is always the chance to get burned. The warning is a typical CYA statement so they aren't responsible for damages cause by the user. Electricity can be funny sometimes. Chances are with the camera off nothing would happen but if something were warned.

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