> but it won't be the correct use of "their", as far as I'm aware.

Yes, yes it will be.

See collective nouns, and "Metonymic merging of grammatical number" https://en.wikipedia.org/wiki/Collective_noun

> this would be incorrect: "the corporations employees went to the summer party" again because "corporation" is a thing

You can easily say "the corporation's financial report for Q4 was worse than predicted".

I think you're focusing too much on specific and hyper-specific rigid rules in a single textbook. As others said, prescriptivism vs. descriptivism. Descriptivism is always better, as it describes how language works and may evolve. Prescriptivism assumes languages are rigid unchanging things that can be precisely described.

The full rules for a working language take people years to learn at universities, and they are never as simple as "an inanimate object can't have a possessive form with 's".

Prescriptivism also works in schools/learning as it helps people not to drift too much from the norm. But too many take it to heart.