I don’t think that’s true? I never did research math myself, but the people I’ve known who do would definitely invest time in making a proof clearer and better even if they had the idea basically correct. There’ve been multiple recent stories of researchers saying “we’re going to publish this lame proof that isn’t up to our standards because the AI companies let us know they’re going to scoop us if we don’t”.
Mathematicians care a lot about the exposition of their ideas, invest a lot of time in giving talks, writing, and don't publish too frequently, compared to other sciences.
They normally don't feel like they are in some kind of race to publish the results ASAP and claim priority. Cases like that are very rare (but they get media coverage because they are so unusual).
OpenAI did a publicity stunt, their motivation is not to make a good contribution to the field, which has very different standards and culture, compared to the AI labs.