Your "wrong but not obviously and completely wrong" line made me think that the "obviously and completely" part is what makes people who are well-versed in a subject demand that everyone should know [knowledge from subject] when they hear someone express obvious-and-complete ignorance or obvious-and-complete wrongness in/of said subject. I've witnessed this a few times, and usually the thought process is something like "wow, it's unfathomable that someone should express such ignorance of something that is so obvious to me. There should clearly be a class to make sure this doesn't happen." After reading what you wrote about compartmentalized knowledge and connected knowledge, this type of situation makes much more sense.