She is also implicitly putting forward herself as a true American, a true southerner, whose family has lived in the county for generations (even if they did so badly and ruined much of what they touched). It is an example of her pretence and the recklessness with which she approaches people. It is also a way of showing just how unmannered she has become: insulting her sister’s husband of whom she is a guest.
Stanley’s reaction is important. He respond to her that he is a true America—self reliant, touch, and irascible. His response is indeed so withering that Blanche is forced out of the audience’s sympathies for the rest of the play (except perhaps until the very end). This confrontation between the two main characters is very important to the themes and dramatic tensions of A Streetcar Named