1. Google wanted her gone, ranging from good reasons (she was too abrasive) to possibly suspect (in this instance she was being abrasive about a paper with ethical questions on Google's practices being stopped from publication with no explanation given)
2. Her ultimatum email can reasonably be construed as a resignation. It roughly said "Do this or I'm quiting", and Google responded with roughly "We're not doing that, thanks for telling us you quit, we accept".
3. This does not follow the typical resignation process used at Google, but that doesn't mean it isn't a valid resignation. It's unreasonable to assume a lawyer didn't look this over before they went ahead with it. The lack of Timnit suing Google for wrongful termination (from what I've seen) agrees with this.
4. Googlers were angry about this situation, because they disagreed with leadership's actions.
5. The leadership's response is legally bound to stick strictly to saying she resigned. This only inflamed #4 more.
6. They were ethically bound to not disclose all details of a situation involving an employee (where as Timnit could paint whatever story she wanted). Even if Timnit gave a full go-head, there were others involved and doxing is a real threat when names are exposed.
7. They were bound by business interests (at its root legal and ethical obligation to the shareholders) to not expose all of the details of the paper, the objection to the paper, and the processes involved.
So was Google in the right here? The situation obviously wasn't handled well. There were clear problems with Timnit, and she did give an ultimatum. However there are reasonable concerns related to "our ethics person gave an ultimatum and we called them on it" - but without the details it's hard to form a nuanced opinion.
Other takes welcome.