The Global Inbox does not exist inside the application any more than your databases do. (This is all well documented in the Getting Started section of the Help and has been this way for a very long time). It’s in the /Library/Application Support/DEVONthink 3 directory or DEVONthink directory for version 4.
So you need to look at your Hazel rule and figure out what it’s pointing at, and adjust accordingly.