No proof of that. He went all out by placing all of his Nature Energy into those last two Rasen attacks, Naruto literally had nothing more to put into them, so he gave it his all. Either Naruto was using killing intent, or Naruto's best isn't enough when he does want to kill. Either way, they evenly clashed.
@Underlined: That's exactly what happened. They both threw their best at each other, and their attacks repelled and injured both of them, hence why both fell from the sky damaged. Naruto didn't want to, but was forced to, which further reinforces that just because Naruto didn't want to use killing intent doesn't mean he didn't.
That's true, but the fact remains that Nature Energy is a replenisher, by collecting all of that Nature Energy, Naruto boosted himself back up to 100%. This is supported by the fact that Sasuke, who can see Naruto's chakra, confirmed he doesn't have enough left for one more TBB, but once the Nature Energy came in, he pulled out two. At this point, Sasuke had used some of his chakra, so if you really, really wanna get **** about it, Naruto had boosted himself back to 100% at that moment while Sasuke wasn't at 100%, and Naruto still failed to put down Sasuke, they still damaged themselves evenly. Every way you slice it, it doesn't go in your side of the argument's favor.