Correct, you can not bring in a character you made when you join another person's game (you will likely be able to customize the appearance of the character you take over, though). In the majority of cases it would be best to have the person hosting the game make the saves.
However, if you get half way through a game playing co-op with someone, and then your schedules get out of sync and you don't expect to be able to play together for the foreseeable future, you would at least be able to each finish the game on your own if the person who joined in also made a save.
If one person usually hosts a game, but their computer or internet connection become flaky, it could be helpful for the other person to save the game so they could host it, and any crashes/disconnections of the first person's computer would not be a big problem. I'm not sure what happens if the host computer crashes, but one of the previews mentioned the computer that join in co-op mode crashes while they were playing, and they simply got control back of the other character.
