I'm not sure that Matt was completely unaware that Survivor players often lie, cheat, betray etc. to do whatever they can to win, unless he's never seen the game. He may simply have wanted to prove that you don't have to be a scoundrel to do well in the game and, unfortunately, found out how difficult it is to do that. I haven't seen every single episode, so I don't want to make any grand statements about Matt's decency or lack thereof, but the fact that his emphasis on his faith may be annoying to some people--and I'm not one who necessarily enjoys people who constantly cite their religious beliefs either--doesn't mean it's insincere or that he's stupid. He may literally have believed that if he tried to live according to his principles, perhaps people would respond to that, even with the cutthroat nature of Survivor. Unfortunately, he landed on Rob's team, and since Rob's game involves completely situational ethics, and Matt was, for a number of reasons, a threat to Rob's game, Rob orchestrated his ouster. Rob may be a completely different person outside the game, but inside it, he isn't trustworthy, because his ultimate purpose is to win, period. Some people find that admirable. Others don't. But I don't think even Rob would deny that's his goal--and that whatever alliances he might form would necessarily be secondary to that. If I were playing Survivor with Rob, the very last thing I would ever do is trust him completely, no matter how he behaved toward me. Of course, I also have zero interest in actually playing Survivor, so there's not much chance of that happening anyway.
Some people are okay with the whole "it's just a game" mentality and others aren't. I suspect Rob falls into the former camp and Matt into the latter. Honestly, I've often wished that there was some other way to refer to competitions like Survivor other than "game," because aside from the rules in the immunity competitions and some very basic guidelines--like don't do deliberate physical damage to one another outside the competitions--there really aren't any rules. Realistically games--whether they be Monopoly or baseball or hide and seek--have rules. You can't just do anything you can think of to win. If you do, you're necessarily going to be reprimanded and/or disqualified.