Thankfully teachers don't usually get their degrees by reading social media posts and whatever else they happened to find on the internet. That said, you should absolutely be paying attention to what your kids are (and more importantly aren't) being taught in schools too.
They don't get their degrees that way, but they absolutely do use social media and have their views shaped by it. ChatGPT is also trained on a lot more than social media, you can be sure it's read a lot of scientific literature as well.
But yes, you're final point is the one I'm getting at: You should be actively monitoring and explaining what your child is being told whether it comes from a human or an LLM.