See near the end of http://www.youtube.com/watch?v=i8z7NC5sgik for an example of how it could. (Short version: I live hear a store that was robbed. I say that I was visiting my mother 200 miles away at the time and I, in fact, was. The police have a witness who think she saw me near the my house, and hence the store, at the time of the robbery. Had I not said anything, a witness claiming I was seen near my house was useless. But given the statement, now that witness would seem to impeach what I said.)