Andrew - I am re-opening this issue as I was sending a Moodle message to someone and the Moodle Docs filter did not seem to be working.
In /message/index.php I noticed:
$messageid = message_post_message($user1, $user2, $data->message, FORMAT_PLAIN, 'direct');
I grep'd message_post_message and it does not seem to be used consistently. I would expect FORMAT_MOODLE to be used in all places (at least by default) as in /user/messageselect.php
Yet in /admin/user/user_bulk_message.php we are using FORMAT_HTML.
Do we want these to all be FORMAT_MOODLE? I figured at least reviewing these to make sure the intended behavior is taking place would be worth a look.
Peace - Anthony