As a certified MBTI trainer in my distant past (along with a foray into conducting workshops on Riso's Enneagram types), I think that there is a lot of confusion about the concepts of introversion and extraversion as descriptors of human behavior. Introverts can be quite outgoing and social, while extraverts can be quite happy spending quiet time alone with a book or being in an intimate setting with a few friends.
MBTI is really about preferences rather than how a person actually interacts with others and with his/her environment. I used the example of right/left handiness to explain the concept in my workshops. Most of us have a preference for using one hand over the other--our dominant hand--but that doesn't mean we can't perform tasks with our non-dominant hand if we are required to do so--for example, a person whose dominant hand is immobilized in a cast. The catch is, for most us, working in our non-dominant hand requires more concentration and effort, our movements are slower and often more awkward, and the end result may not be as good as if we had been able to use our dominant hand. With effort and practice, though, many people can train themselves to become ambidextrous to the point where a casual observer might not be able to detect any difference. The preference hasn't truly disappeared, but a person isn't as affected by his/her preference as is someone who has only ever worked with his/her dominant hand.
If you think about introversion and extraversion as preferences, rather than labels, it makes sense that many people actually do train themselves to be ambidextrous, especially if they are in jobs or environments where a particular preference is considered to be "better". Generally North American society is geared towards extraversion, so those who have a preference for introversion often choose to be "closet" introverts and learn from an early age to display many of the extravert preferences. In other cultures, or circumstances, an extrovert might learn how to "tone down" his/her preferences to fit into a set of family or job expectations.
And just a couple more points. Strange as it may seem, figuring out a MBTI preference isn't always that easy; it's like trying to figure out one's style preferences--I should know how I want to dress myself, but the more I think about it and explore options, the more confused I get. Many of the statements on tests of extroversion vs. introversion could be truthfully answered "it depends" because most of us have learned to morph and adapt to different circumstances. It can take quite a bit of thought to differentiate between what I can do from what I might actually prefer.
It took me quite a while to realize that I was a "closet" introvert because I felt much more comfortable being an extravert professionally and socially. Most of the descriptors on popular E vs.I tests place me squarely in the extravert end of the continuum, but my true preferences lie at the opposite end. For most of my life, I worked and played "in my other hand" since performance always trumped preference for me--and I've come to realize that I'm not alone in doing that. As I used to tell my workshop participants, though, learning that about myself was much more useful than trying to figure out which label I ought to put on my forehead.
ETA: And just one more thought: My sister is a true MBTI extravert but even she needs time alone to re-charge from her public, demanding job. She lives alone and loves being able to retreat back to her place at the end of a busy day. She also is choosey about her friends; she wouldn't be happy sharing a room with someone she didn't like or know very well. I guess my point is that all of these characteristics that seem to point towards introversion actually are more about an individual's personality, circumstances, and tastes than about extraversion or introversion. As I said, it's complicated.