Keep your cool
Rich,
I feel your pain and frustration, but you MUST keep your cool. One place to go is HR. They are already aware of the difficulty between you and your supervisor, and apparently have backed you up at least once. But you really need to present your case with a sort of detached professionalism. Have documentation of your position (Rebecca's links were excellent), be convincing but NOT passionate. If necessary, role-play with a trusted friend.
Reading between the lines I'm getting the sense that your emotions (frustration, anger) might be showing through. You mention your "passion for doing things right." Messages delivered with a "confrontational" (to use your supervisor's term) attitude are rarely heard, and the perceived attitude can lead to disciplinary action (including termination). So be as careful about the way you deliver the message as you are about ensuring the accuracy of the message.
You will always come across those people who cannot accept an idea that isn't their own. The most successful people find a way to let the other person buy into the change or even think it is their idea. If your supervisor believes you are confrontational, she will be defensive. If you can give her some slack so she can approach her supervisor with a change that is "her" idea, she may be more receptive. Try going to her with the supporting documents and just say, "Here's some additional information that you might find useful when you take this to your boss. If there's anything else I can help you with, just let me know." Deliver this message with a smile and a pleasant, helpful attitude. Then leave the room.
Finally ... all this talking about who said what, when and to whom, and how someone looked after a meeting is distracting everyone in the department from doing their jobs. I've seen office dynamics like this, and they can turn really toxic. Do what you can to stop it; try not to let it affect your job performance.
And keep looking for another position because I sense that in the long-term this will not be a good place for you. That will be their loss, not yours.
Hope that helps.
F Tessa Bartels, CPC, CEMC