You are, of course, correct. The main issue isn't with writing them down but with people finding them if they are written down.

This means not putting passwords on a post-it on the monitor and to guard them like you guard your wallet or house "keys", wherever they are written down or otherwise recorded.

Of course, with so many passwords in one place, it's best to do a little planning in case a paper gets lost or wet. It's also a good idea to consider what might happen if ALL passwords get disclosed at once.