MadMonkey: There is a big difference. A private challenge is sent to only one team, so there is no doubt which fellowship will accept it, so it can be done by any person with the proper rights (captain or boss). But, if you are a Big Boss in two fellowships and a captain in the third one, and open a public invitation, which fellowship should be chosen as the opponent?
That's why only a captain can accept a public invitation because he cannot be a captain in more teams of the same game.