Introvered vs Extroverted is probably the most rock-solid part of MBTI.

Interestingly enough, Briggs work was based on Jung's research that lead to Psychological Types, the 6th book in Jung's Collected Works. The book, aside from the definitions, has 10 chapters. The first 9 deal with Introvert versus Extravert, and the 10th deals with how they are affected by the 4 function types.

However, psychologists are using the terms in a very strict sense, removed from the connotations we normally attach to the terms.

That's a bit misleading. Psychologists invented those terms, and the connotation we use happen to be the effect usually seen from them. Not all Introverts are shy, and not all Extraverts are bold.

Specifically, it's if you take your energy from inside or outside.

That is Keirsey's definition, not Brigg's. Keisey's definition has more to to with practical applications than what it actually is. Jung, who defined the terms as we use them today explained that Extraverts are objective to the world of people and things, (and by extension, subjective to the world of ideas). Introverts are the exactly the opposite.