Well. Let's just think about this, assuming no red herring was involved.
If the issue was about Catija powers the specific site would not matter, right? Suppose that the trigger was "vote in an election" - a staff member can't get that hat because they can't vote, but they can't vote on any site.
Since Catija mentioned Code Golf specifically, the problem must be related to that specific site. So, either that site lacks something other sites have or this is about some action she would not do on that site for personal reasons. Rep based privileges should not be related since as a staff member…