Some anal Captains want a ‘pristine’ logbook. So they have the mate write everything down on a scratch pad and then later the Capt goes back and enters the info in. The process is called ‘rough log’ (scratch paper) --“smooth log” (formal logbook)
Most ships use this format. Maybe this is where your guy learned this from?!
You mentioned that he says: ask if you want to see it. That sounds like it is open for inspection to me. No?