Yeah, you need people to have your back, because ultimately when it comes down to the end you need to convince another faithful that you're true and someone else is the traitor. But it's more important to not stand out for ANY reason. Saying you've rejected a recruitment would raise suspicions.
And what I mean about it not being a team game is, ultimately, if it's not you winning, who really cares if it's traitors or faithfuls at the end.
Why give up information that helps the other faithfuls if by doing so you're putting your neck on the line.
Same with if you work it exactly who a traitor is. Don't blab to the group. Keep quiet until nearer the end when you feel more confident about who you can trust.