It sounds like OpenAI is trying to appease the author when they don’t have to by allowing him to rewrite their proof. They probably don’t believe he deserves to, so him asking for a coauthor from Anthropic might overextend their grace in their eyes.
Now maybe LLMs can also simplify arguments and make sense of them for humans, but we haven’t seen that yet (unaided).
(I haven’t looked at it, personally.)
They don't need any help publishing.