Today, what most people mean by an "extrovert" is someone who's very outgoing and social, while an "introvert" is typically seen as a shy loner.
But for Jung, who coined these terms, an extroverted person was one interested mostly in the world outside of himself, while an introvert was interested primarily on what was going on inside himself.
Jung would have seen no contradiction in introvert who was very gregarious and outgoing, if he was mostly interested in his inner world (since it would be the latter quality that made him an introvert).
Likewise, Jung would have seen no contradiction in extrovert who was very solitary and shy, if he was mostly interested in the world around him (since it would be the latter quality that made him an extrovert).
Now, as for whether this is a "myth" or not is a matter of opinion and debate. Psychology is far from a settled discipline, where all participants agree on the "great truths" like "the law of gravity" or "the laws of thermodynamics". There aren't any such things in psychology, since there are in fact many different psychologies, with radically different explanatory frameworks. What is a myth to one psychologist might well be established dogma to another.
Also, the division between introverts and extroverts is a Jung-era myth which got picked up by Myers-Briggs. Extroversion is a continuous variable (with most people being neither introverts nor extroverts), and is also contextual.
If people think there's a silver bullet for dealing with people (called "EQ" or "extroversion"), they're. EQ is a broad set of skills. They are probably correlated with general intelligence, but not strongly. I doubt they are all correlated with each other - in some context a certain trait (say - assertiveness) is a big advantage, in other contexts it can be a disadvantage. Some people are great in some situations, some people are flexible, and can adjust to many situations, and some people are losers in many situations, but it's not simple.
So I like that you've suggested a lot of different resources.