Zen~
You have just described my sister to the detail., (with the exception of the neatness).
My sis has to be right in everything. She absolutely demands it. There was a time in our early adulthood that she was so bad that I went as far as to print out a certificate of completion to the Academy of Knowology as the student with the highest degree of being a Knowologist.
I'm sorry that your friend is as such. You have every right to feel as you do regarding your friend. I know how exhausting it is to try to maintain such a relationship.
There for a while it got so bad between sis n self that I quit communications with her entirely....lasted a good 2 years. We gradually reunited, but this time I tried a completely different approach. I allowed her to believe she was right...about any and everything. I quit arguing with her and anything that I wanted kept secret I certainly didn't tell her.
Because she's my sis and I do love her so much, I couldn't simply just forget about her. The break apart did do us justice though.
Depending on how important this friendship is to you should determine if you feel you are at a loss with her. As it is, I wouldn't expect much of a change from her, unless you are willing to express to her your concerns and perhaps include some ideas as a means of solution in order to salvage your friendship. Of course, that depends on if she isn't so offended that she doesn't accuse you of attacking her with such slander first, (sis was extremely defensive of herself, as well).
I hope the best for your situation with your friend.
Communication is the most important thing here, but with her unwillingness to be receptive, it just may be more difficult than not for you.
Take care~
Shangrala