The way I see it, so much about this hassle seems to point towards some fundamental misunderstanding about what their job was - that perhaps they believed, like you say, that their job was to call out the company and others on AI ethics issues, but that the management who formed and funded that team believed that their job was something else - I think that what Google wanted from that team was to do research on applied methods on how to make the models less biased and on process improvements on how to deploy them in a more ethical manner - i.e. to work on technical solutions to mitigate the ethical problems they identify, to enable Google to achieve the same goals through ML but with less ethical "side-effects" so to speak.
For a specific example, I presume Google would be happy if the team produced methods that help facial recognition generalize better to different ethnic groups, or methods that identify what specific gaps in training data should be filled to cover a diverse target audience; but apparently did not consider highlighting problems where the only solution is "don't deploy such models" and social activism goals as their intended job.
So when the push came to shove, this misalignment of goals had to be addressed; either by one or another changing their goals (which seems to have been unacceptable for both Google and Timnit&co) or by firing/quitting.
The unit was full of Academic researchers, who regularly published papers and collaborated with others on papers; the whole kerfuffle started with Google's uncharacteristic request to put a lid on Dr. Timnit Gebru's paper. To me, that doesn't sound like a team that expects, or is expected to just work quietly on internal - likely confidential - projects.
I suspect Google leadership were on board, and wasn't even aware of the misalignment until Dr. Gebru declined to pull a paper that raised questions on a crown-jewels-level, Jeff-Dean-supported AI model that materially impacts Google's finances (and likely some leaders' bonuses too).
Now that Google leadership is aware of the misalignment, I think its actions show the direction they are taking going forward.
For a specific example, I presume Google would be happy if the team produced methods that help facial recognition generalize better to different ethnic groups, or methods that identify what specific gaps in training data should be filled to cover a diverse target audience; but apparently did not consider highlighting problems where the only solution is "don't deploy such models" and social activism goals as their intended job.
So when the push came to shove, this misalignment of goals had to be addressed; either by one or another changing their goals (which seems to have been unacceptable for both Google and Timnit&co) or by firing/quitting.