I would have stated this a bit differently: No amount of running or testing can prove the code correct. You actually have to reason through it. Running/testing is merely a sanity/spot check of your reasoning.
You can't just rewrite everything to match your style. You take what's in there and adapt to the style, your personal preference doesn't matter.
Writing is a very solid choice as an approach to understanding a novel problem. There's a quip in academia - "The best way to know if you understand something is to try teaching it to someone else". This happens to hold true for teaching it to the compiler with code you've written.
You can't skip details or gloss over things, and you have to hold "all the parts" of the problem together in your head. It builds a very strong intuitive understanding.
Once you have an intuitive understanding of the problem, it's very easy to drop into several different implementations of the solution (regardless of the style) and reason about them.
On the other hand, if you don't understand the problem, it's nearly impossible to have a good feel for why any given solution does what it does, or where it might be getting things wrong.
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The problem with using an AI to generate the code for you is that unless you're already familiar with the problem you risk being completely out of your depth "code reviewing" the output.
The difficulty in the review isn't just literally reading the lines of code - it's in understanding the problem well enough to make a judgement call about them.