I would think that most are "scripted," at least to some extent (probably much more so, than the producers would like for the audience to think), and since the "competitions" are set up, the director can sort of guess where interesting stuff will happen, and set cameras there.
Rod (Able123) would probably be a good person to comment, as I think that he has been a grip on some "reality" shows.
I doubt that they just video everything, from multiple angles, and then edit the cinema verite footage, as they would have 100's of hours to go through. It would be like Rod's Elephant Hunt video - walk though brush, stop and listen, walk through brush, stop and look around, walk through brush, stop and scratch, walk through brush, etc., etc., etc. Or perhaps Andy Warhol's Sleep.
Just my thoughts,