Was HMS Enterprise considered for HMS Victorious's American voyage?

Is the story that HMS Enterprise was considered to accompany HMS Victorious to the United States a myth, and who originated it?

Enterprise was one of several options considered. A U.S. upgrade would use 5-inch guns, but her existing usefulness made a C- or D-class cruiser a likelier choice. No originator is identified.

HMS Enterprise is identified as one of several options considered to accompany HMS Victorious to the United States. An American armament upgrade would use 5-inch guns. Enterprise's usefulness in her existing configuration weighs against undertaking the conversion. A C- or D-class cruiser is judged more likely to have been sent for that sort of upgrade. No originator of the Enterprise proposal is named.