In my experience (both as a child being taught, and as an adult working in schools) teachers often give wrong information. It's very very common.
How you deal with it depends on the teacher. Some teachers have the whole pride and power thing going on, and they become resentful if they are corrected, particularly if they are insecure - they could then take it out on the child in subtle little ways. I talk from the experience of having corrected my teachers quite frequently when I was a kid - in my naivety, I assumed they'd be delighted to be given the correct information/grammar! ;D In reality, of course, quite a few resented me for it. When I was 6, I had one teacher who did not take kindly to me correcting her grammar (to be fair, I hadn't been very polite about it - I told her she was stupid! Although, in my defence, she was!), and who then made a point of regularly ridiculing me and getting the class to join in. Some teachers, however, said they'd check what I'd said, and then came back to me the next day and told me I was right and then informed the class that the information they'd given was wrong. These were the minority. They were the best teachers though, and I guess my approach reflected this - I didn't tell them they were stupid, because they weren't!
In short: intelligent, open-minded teachers, who are more interested in learning than in needing to be right all the time, will be receptive to being corrected, and glad to learn the facts. Insecure teachers who are control freaks, have big egos, and need to be right all the time, will not be so receptive. Unfortunately teaching is a career that attracts quite a few of the latter - but fortunately a few of the former too. The most important thing you can teach Chey is the fact that her teachers won't always be right, and that she should never assume something is right simply because a teacher said so - encourage her to check things for herself. That is way more important than whether or not the poster uses the correct information or not.