We think very much alike. I love being alone every once in a while, because I'm alright with myself. People who fear loneliness fear being alone with themselves, with their thoughts, with nobody that tells them what to be, what to like and dislike, what to think.
Thing is, only when you feel that you don't need other people you can establish healthy, strong relationships with them. Then you can share those "internal dialogues" and get those travel companions that you talk about.

I don't know if or why people confuse these two concepts. Rejection is, basically, forced loneliness; if you are afraid of loneliness, I guess you might feel rejected everytime you are alone. Or maybe, if you don't like yourself you get convinced that society doesn't like you either.