Should a unit test include the converse of what you are testing?

Imagine that we have a game with different types of servers in it to represent different countries. Now, lets say the game only allows users to "buddy" other players that are only in the same server that their account is attached to. As a developer, I am tasked to write a test case only to see if the feature for users to "buddy" one another works. However, here is where my dilemma lies, since I only have to test whether or not a user can "buddy" someone else, do I have to also test if the user cannot add users from another server in this same test case, or should that be written in another test case totally separate from the current one that I am writing?