This may very well be the case today, or in our society, but it's not really difficult to imagine a society in which you have to 'hold' really crazy idea in order to win. Also, believing true things is an endeavour which is never completed per se: it surely is not possible to have it sorted out simpliciter before attaining 2 (the third imperative I really see as a subgoal of the second one).

The thesis after all conflicts with basically all history of humanity: homo sapiens has won more and more without attaining a perfect accuracy. However it seems to me that it had won more where it accumulated a greater amount of truths.

So I won't really say that in order to win you have to be accurate, but I think a strong case can be made that accuracy enhances the probability of winning.

What is then the real purpose of rationality? I'm perfectly fine if we accept the conjunction "truth /\ winning", with the provision that P(winning | high degree of truth) > P(winning | low degree of truth). However, if Omega is going to pop-up and ask:

You must choose between two alternatives. I can give you the real TOE and remove your cognitive bias if you accept to live a miserable life, or you can live a very comfortable and satisfying existence, provided that you let me implant the belief in the flying spaghetti monster.

I confess I would guiltily choose the second.