There is no problem as far as I can see. To prove this for yourself plug in a headset and listen. Talk so the area mike or a boom mic picks up your voice, make sure the parking brake is set, and push the erase button for half a second or so. You will hear a tone indicating that a bulk erase is in progress. If you hear this tone the CVR is not recording.
The CVR is powered up whenever the CB is in, as is the FDR. Just because they are powered up and are been fed data does not mean they are recording it.