AFAIK in every US state a company can fire you for any reason that’s not protected, and “we told you this was okay but changed our minds” is as good a reason as any in the law’s eyes.
Correct. If she had something in writing, signed by a person with proper authority in the organization, she might be on stronger footing. But they could just find some other reason, or state "no reason" for her termination, and that's perfectly legal in an at-will employment.
In many US states a company can fire you even for protected reasons, and just fabricate a reason that isn't protected. Of course there are examples of people fighting this because it sometimes is a fight worth having, but the vast majority just have to accept being discriminated against and try to find another job.