There is not even the testimony of that person. They don't told you what she say, they don't allow you to confront her.
For all that you know they could be making up all the thing. I don't think this is the case, but it's a possibility when everything is done in the dark.
Don't take this as advice, please, because I can't predict the results, but in your position I think I would feel compelled to confront them. Maybe with the help of some worker representative if that it's available to you. What I would avoid is to confront the woman, that could backfire very fast.
My actual communication skills were not the issue, mind. The company frequently asked me to write and give presentations, either in public conferences or to the rest of the firm.
Anonymous accusations that sink careers are a plague of the modern workplace and are entirely due to a culture of "always believe the victim".
Question: did they provide you with any substantial evidence?
Anyway, ultimately your case and many others is why the law is at it's very core based on an innocent until proven guilty paradigm. Once you take that principle away, you put all the power in the accuser and none in the accused, which is objectionably unjust.
I've recently seen a few very disturbing comments on HN and from similar people (above-average education, born into privileged conditions, politically left, etc.), who naively believe that this is a bad or somewhat ineffective paradigm, and that we should "just believe" rape accusations, because ???? shrug. It disheartens me that some people can be so blindly ignorant about the law and human nature. We only need to take a short walk down history lane to explicitly see that if you give one side of anything human-related an enormous amount of power (like in this case if accusers are believed before evidence), there will be many who abuse it. It is human nature, and the law prevents it from reining free and causing utter chaos.
In your case, by the sounds of it they did not present to you any form of evidence (right?) to show you your misconduct. No sexually harassing text transcripts, no internal email transcripts, no witnesses, nothing. What this is is chaos and injustice, under the guise of some very malformed concepts of "progressiveness", and it's unfortunately ever-more prevalent.