Assign call timeline entry limited to owner (I think)

[JJack]

We have a call, raised via self-service, where the owner has changed without this being generally visible in the timeline. I'm assuming this is because the visibility was limited. However I'm struggling to find what set-up allows the visibility to be limited to, say, Owner. (This would have been a manual change, not via a process).
I can see for one call, that I raised not via self service, that Owner is an option if I go to reassign it but this is not the case for my other calls and  I don't understand the principle that's at play here. Can anyone help?