From experience (as a bystander), what really happens in a case like this is:

* Employee is terminated

* Employee believes they were terminated for a reason forbidden by state or federal law

* Employee retains an employment lawyer, who drafts a letter demanding compensation for the improper termination, citing specific claims of (say) sexual harassment, complaints articulated to superiors and to HR, and subsequent retaliatory firing.

* Employee does not necessarily prove those claims; they need only demonstrate sufficient facts and allegations to ensure that a lawsuit would not easily be dismissed.

* Employer almost invariably settles.

The two cases where employers don't settle:

* Employer is stupid, and believes that they will pay less to litigate a wrongful termination case than to settle.

* Employer is smart, and has an HR department that keeps excruciatingly careful records of things like sexual harassment complaints, alleged racially-tinged comments, ratio of black/white hires to black/white applications, &c, and is prepared to make it clear to employee's lawyer that the case will cost too much to pursue.

If you've ever wondered why smart employers go fucking apeshit when people make racially-tinged jokes, or why it's not necessarily in your best interests to bring your concerns to HR unless your game plan is to bring a wrongful termination complaint, there you go.

This is also the reason why, despite at-will status in basically every locale where you can hire people, "Performance Improvement Plan" is a euphemism for "slow-motion termination". The purpose of a PIP is to establish in the written record that an employee is a non-performer, so that when they're terminated, the employer can present evidence that there were reasons other than retaliation or discrimination.

It's called court. No provided reason does not imply a lack of reason, and (say) discussing pay on a public forum would certainly be relevant evidence, if highly circumstantial.