Not exactly,

They said that they APIs were copyrighted, and that the way that Google had reimplemented the API fell under fair use doctrine (the original work was still copyrighted and they were allowed to use it without authorization).

As for using an LLM to reimplement a program, you're going to end up with a derivative work which can only be created/authorized by the original copyright holder. If you don't have the authorization, you are infringing on someone else's copyright.

If however, you used an LLM to read a program's source code, sort each word alphabetically then output the result, you're going to have something that while based on an original copyrighted work no longer functions as a program. It has been transformed to such a degree that it is considered a transformative work, and thus falls under the fair use doctrine.

TL;DR: Simply getting an LLM to regurgitate source code back out to you does not remove the licence of the original source.

Thank you: I hadn't known.

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