Oh do I ever know that type. Mucho sympathy. And nice of you to try to stand up for your coworker. Won't accomplish much -- boss is in "must save face and show them who's in charge" mode -- but nice of you. I doubt that she really doesn't know she's wrong, she just has an unnatural fear of
admitting she's wrong. Is she, like, short, young, extremely stupid? (The last one seems to be indicated by your story.) At any rate, I'd bet she is pretty insecure for whatever reason.
There was one time when I wanted to get a special, hard-to-get, prestigious certification for my program (before I went solo.) My boss said, "no", I asked why, and she said "because it's too much work." I said, well,
I'll do the work, and she said OK, great. So I assembled this BOOK full of sample lesson plans, special forms I had to create according to their guidelines, etc., etc. It was a TON of work. As I was finishing up, I found out that my sister-in-law, who was 9 months pregnant, had been found to have a brain tumor and needed to be operated on immediately. My husband and I arranged to leave the next day to help out with everything and help care for the newborn. (Delivered by c-section so s-i-l could have brain surgery.) The deadline for the certification application was later that week -- I was leaving Tuesday, it was due Friday. So I worked extra extra hard to get it all finished. Definitely a Scotty "Well, I need a minimum of 8 hours..." [4 hours later, as they're about to explode] "there! It's done!" moment. Almost missed the plane in the scramble.
But, finished. Absolutely all the way every last page finished. Whew. Felt good.
Made sure the boss got it in time, went to tend to s-i-l (she came through it fine, baby came through it fine, everyone's healthy now), and then waited to find out if we'd actually gotten the certification. Expected it. Was taking a long time. Asked the boss. She was cagey. Started to get suspicious. Then, in a staff meeting, with about 10 other people, she rattled off quickly at the end of something else, "Oh, and I made an executive decision not to submit the certification application." WHAT?? I told her off, civilly but in no uncertain terms, in front of all of these people (which I guess she had been betting I wouldn't do.)
Found out later she thought I'd never be able to complete the application in time, and just said "yes" so she could blame it on me when it wasn't finished. Never wanted to do it. (Cost $200 or something, but would have paid for itself many times over.)
Some people...