Well, you're taking it at face value. :) Other LOST fans have commented on what Charlie said, and it turns out later that Charlie is an experienced swimmer after all. So, it's kind of a half-lie. "I don't swim" is a conscious choice not to swim, but if he said "I can't swim" he would be lying completely. Given the situation at that moment, people may assume "I don't swim" means "I can't swim", but Charlie didn't say "can't"... see? :)

Two thoughts on "I don't swim." 1) You could consider it to be a shortened version of "I don't know how to swim." and 2) It is the simple present, which implies a habit (or in the negative, the absence of a habit). "I eat donuts on Tuesday" for example, means "I eat donuts usually every Tuesday." Similarly, "I eat chicken." can mean "I make a habit of eating chicken from time to time." So "I don't eat chicken." means "It's my habit not to eat chicken." That would make "I don't swim." a kind of euphemistic way of saying "It's not my habit to swim." meaning that you swim poorly or can't swim at all. So the difference between "I can't swim." (absolute inability to swim) and "I don't swim." can be one of degree. "I don't swim." *almost* implies that if I tried really hard, I might be able to swim a little bit. The difference is more marked with something like "I can't read novels." and "I don't read novels."

People do sometimes say 'I don't' for certain situations when they mean ' I can't' eg I don't drive. Maybe it's because they are embarrassed about the fact that they never learnt, and are trying to imply that it's through personal choice rather than lack of ability?