“Or do you disagree with this assertion?”
In the Florida companies where I worked there was, in general, a strict protocol. You called someone in and talked about whatever deficiency and then agreed on a corrective action plan which had some suspense date. Then you called them in and discussed and documented what had happened according to the plan. Then, if they hadn’t done or had violated whatever previous plan they’d signed, we’d walk them down to HR and it was all handled as part of a process. If that’s the process you follow, it’s pretty hard to “lie” about it.
But what no sane company would do is fire someone without some process and documentation. What that is in this case probably won’t come out without a lawsuit. Sane companies are loath to say or release anything to the press regarding someone’s termination. Having said that, I have seen individuals in a company do some incredible things. One manager fired someone while telling him in front of witnesses that he was just too old for the job. (That was one ugly lawsuit.)
To answer your question, companies do not, in general, say why they are firing you.
Could somebody in the company have said, “Yeah, we’re firing you because you have a MAGA bumper sticker.” Whoever did something like that needs to be fired. Likewise here, yes it’s a possibility her story is true. But if that was the reason the company best keep it quiet.
“...whatever deficiency...”
That’s where things have gone sideways.
Companies or organizations of any size no longer possess a shred of integrity along the lines of what one would expect to find, for example, in a confirmed Catholic adult man.
Hence the profusion of “pretextualusm” in HR, any counseling or disciplinary process in which HR has a hand, and the termination process.
It’s a new day.
A word to the wise is said to be sufficient. People need to wise up