Answer: Not necessarily. Si is 'traditional' in the sense that it focuses on past experiences, and that differs from person to person.
Let's take a hypothetical- let's take it back to high school as a background. If an ISTJ was to look at his classmates he'd likely assess them by what they are involved in and who they hang with. So he might see the jocks and conclude that all they are interested in is sports and goofing off (based on his storehouse of information about athletes). ISTJ hates sports and is a serious student. So he'll avoid any unnecessary interaction with them, at the expense of his fitting in, as his Si may also assign their activities as what's necessary to fit in. He could want to fit in (normal for a lot of teens), but if that's what it takes to fit in, then he'll gladly stay out of place.
Being introverted isn't a hindrance to fitting in, btw. Using the above, there could be an ISTJ among the athletes, and although he may not be as gregarious as his more extraverted teammates, he fits in because his experiences are in line with this group. The athlete ISTJ may not consider themselves fitting in, though; he'll feel this is his group of friends and nothing more.