As I have 2 levels of moderation, this won´t work.
Instead of placing the field where I wanted it, I placed it in the tab where I wanted it as display only, and set CB Conditional to view it only to the highest level User group.
This works just fine now!
I guess I could have created another dependent field with another access level, and populated it with Auto Action on save, but that feels a bit overkill.
Please mark this thread as solved.