Render Props and PureComponent docs question/improvement opportunity

https://github.com/reactjs/reactjs.org/blob/b4b68460e2377837df6e1826e77af173dc205f4f/content/docs/render-props.md

In the above link, the last section ("Caveats") talks about how one can avoid killing PureComponents benefits by pulling the render prop function out into an instance method. I understand why this is the case; the 'anonymous' function 'pointer' would change every render, so it isn't seen as something that didn't change, and the PureComponent would re-render all the time.

However, it says you can't do that with a PureComponent if the instance method / render prop needs to reference the component's state/props:

In cases where you cannot define the prop statically (e.g. because you need to close over the component's props and/or state) <Mouse> should extend React.Component instead.

I don't really understand why that is a limitation, so I'm proposing this as both a question and a suggestion for an update to the docs. I've never used or really looked into PureComponent, but from a look at the docs for them it seems like they re-render if a shallow comparison of it's props/state shows a difference. If that's the case, why wouldn't an instance function on Mouse that used it's own props/state work with PureComponent? The Mouse would re-render if one changed.

(Is it because the Cat - the child component of the render prop Mouse - wouldn't re-render, even though it's parent would?)

content/docs/render-props.md を読み、特に最後の「Caveats」セクションと PureComponent に関するガイダンスを確認してください。props または state を使用するインスタンスの render-prop メソッドが PureComponent と互換性がないと説明されている理由を明確にし、子のレンダリング動作が関係するかどうかも説明してください。ドキュメントがこの疑問に直接答え、関連する制限を説明していれば完了です。