> Our research shows that LLMs are not yet capable of self-correcting their reasoning
The paper actually just shows that the particular "self-correction" strategy and set of prompts they used doesn't help for the tasks they looked at, for the models they looked at. It may be the case in general, but it may not.
> it is plausible that there exist specific prompts or strategies that could enhance the reasoning performance of models for particular benchmarks
Seems they agree. So the wording of the title/conclusion is too strong.
> searching such prompts or strategies may inadvertently rely on external feedback, either from human insights or training data
I'm not sure this justifies picking a single prompting strategy, and not looking at the impact of different prompting strategies. Even just writing a few different prompts in advance with different wordings and showing the variation in results would have been helpful.