Can you explain why your view, which is the opposite of the OP's, is correct?

"RL training directly raises the success probability , by spending a lot of compute on searching for successful paths and then training the model to reproduce them. The gains we credit to “thinking longer” come from the search we paid for during training, rather than at inference."

Not mutually exclusive. LLMs are kind of like a self-fulfilling prophecy. Once some technique is discovered, it'd be part of the training process and becomes more efficient.