First of all, let me whole-heartedly agree with your final statement! I work in K12 education. Teaching students how to be good researchers is one of the most important skills students can acquire and – in my opinion – more important than any single course’s breadth of content. We have to teach that skill and need to do a better job than we currently do.
Second, I’d caution about painting with too broad a brush when saying library stuff is accurate and Internet stuff is iffy. I won’t elaborate other than to provide this article: https://www.nature.com/articles/438900a which does the elaboration for me.