The override option is not present in the "Enable automatic completion" function, but only in the "Complete" function from the drop down menu:

There they should see the "Override branch policies and enable merge" selection. Also the merge type can be overridden.

But perhaps you already knew this, but anyhow your screen capture was from "Enable automatic completion".

If the reason is still about permission settings, you can download the full security definitions from branch policy settings:

and search if there is any group where the user could belong where "Bypass policies when completing pull requests" is "Deny".