Believe it or not, it's illegal for companies in the US to prevent employees from discussing their salaries.
If they reply "Because you are brown"
Instant lawsuit, lots of money.
If they reply "For bad work perf", and it was really for poor work perf, they are fine.
If they reply "For bad work perf", and it really was because you were brown, and you prove it, lawsuit. It is obviously hard to prove. One way may be to show "Look I had 12 performance reviews, on all 12 I got perfect. In fact I did better on my perf reviews than people who are green, so obviously there is a bias for green people and against brown people.
Which as you see, the entire argument hinges around the exact reason you are fired. This is why when people are fired, it is safer from a legal standpoint to not give a reason. Even though that kind of sucks for self development. If you really were fired for being a jerk to coworkers... it may be nice to know that, so you can work on it at your next job.
Companies don't want their reasons for firing people in the public. If they said they fired her for performance, she could subpoena not only her own performance history (Google has secret "calibration scores" that are not shared with the employee) but the ratings of others in the company and any HR actions taken toward them-- in order to find out if people were evaluated consistently.
No company wants its HR data in discovery, because almost every company has dirt. They'll usually settle.
- It is not required for a company to facilitate it.
- It is not a priori allowed to use company resources to discuss your salary.
- As a company you do not have to reward that unprofessional and irresponsible behavior.
What this Google employee did was obviously toxic for the culture. As a manager, deciding who gets the raise and who doesn't is already a hard decision (as Ben Horowitz says: Both actions will make some people feel left out), without your employees trying to undermine that.
I do not think this had anything to do with her being a female. If a male had set up an internal mailing list questionnaire he would have probably found himself in the exact same situation (people higher up do not like it when you are a trouble maker). How she leaves it ambiguous and yet hints at pay inequality for women at Google is lacking class and tact.
Google wants more equality. All things equal they hire minorities. If HR analysts find statistically significant inequality I doubt they would ignore that.
You don't use internal mailing lists to promote your religion, just like you should not use internal mailing lists to promote thorny political/social issues.