No, its not.
> Gebru tweeted the name of the employee
Sure, more to the point Gebru tweeted that Mitchell’s corporate email appeared to be nonfunctional, sure.
> Axios then reached out to Google
That seems likely to be the sequence of events, sure.
Usually and ethically, a company that was in exactly the circumstances Google described would have:
(1) Declined comment, or
(2) Confirmed the email was nonfunctional and declined further comment, or
(3) Explicitly declined comment on personnel matters (especially if the framing of the question from Axios raised the issue of it being a disciplinary action of some kind; raising a personnel issue when it wasn’t part of the framing of the question would itself be somewhat unusual.)
> Context matters.
As an abstract truism, sure; while the narrative you describe is exactly what seems like the most likely scenario to me, I didn’t describe it because that fact was already considered in the description of scenario #1. Google’s behavior is (even assuming that they are being completely honest) grossly unethical in the context described.