When a mod edits another user's chat message, it doesn't seem possible for that user to make changes to the new revision.
Steps to reproduce:
- Post a message in chat.
- Have a(nother) moderator edit that chat message.
- Try to edit that message yourself. The text area will now contain your own last version of the message, and will not reflect the mod's edit. It doesn't matter whether you edit via the message actions menu or via up-arrow.
The problem is fixed when reloading the page, so I guess the previous version is cached on the client side and not updated when someone else makes changes to the message.