Just a thought:

What if Perrin already saved Rand for the second time? Rand was in danger at Dragonmount and Perrin was there. I'm not saying this is the case, but it's something to consider. If he did somehow save Rand what did he actually do? Was Rand so close to tipping that Perrins presence in the Dreamworld could've been the nudge that made him go the right way?