I think I found something related to this original issue and possibly its cause, and also why Patrick could not reproduce it.
When I am editing Java file "B", the Messages tab shows a live error in another file (file "A") that no longer exists, I fixed it long ago.
However if I copy my entire project directory structure somewhere else, reload it and open the file "B" in that project, I don't see this live error anymore.
Going back to the original project: even if I right click "delete" on the live error, if I switch to another file, then come back to file "B", the old live error comes back again even though I "deleted" it.
How to "delete" it for good so it stops showing up? Is it cached somewhere?
To try and answer my own question, I searched my config directory for a string in the error message and found a sub directory "java_rte_classes". I closed SE, then deleted the "java_rte_classes" directory, and now this false live error doesn't show up anymore when I relaunch SE on this project and view the file.