A writer hired to write the wording on Google's websites could submit a change that rot13s every word on Google's web properties. This would not be against the law, additionally it would be exactly what the employee was hired to do. But the employee should be fired all the same.
Also the people arguing for giving the employee a "talking to" instead of firing I think are not considering the game theory aspect to this.
If the precedent is "a talking to" with future offenses resulting in a firing, then smart Google employees will realize that they can create an internal activist email list, get new hires to join it, and then when an opportunity for activism presents itself get an employee with a clean record to perform the activism, rinse repeat.
Of course the message in this case wasn't terribly harmful, so I'm sympathetic to the argument of "it's not such a big deal". But the problem is, Google doesn't want to wait for the big deal (for example a chrome extension change to search exec's TextAreas for keywords a "whistleblower" might want to report on) to actually happen and then fire them. They want to prevent employees from thinking they should ever try doing that in the first place which means putting the foot down before the inevitable happens.
Yeah, in terms of what she did I would agree it wasn't terribly harmful; and I applaud her for taking a principled stand. I just don't really blame management for saying: that was a step too far, you're out. I mean, unionizing is a super sensitive topic at any company, and by adding the message to the tool it added extra weight to the message by making it look like it was endorsed by the higher ups, rather than being a message from a 21 year old. There's no way management is going to be happy that someone is essentially acting as their voice on a topic that is very sensitive.