Having being separated at birth, the twins managed to meet up with one another later in life. However, the two didn't realize they were related by blood and proceeded to fall in love and get married.
Sounds like your typical anime/visual novel right? Only thing is, this happened in real life. What you've read earlier is true, although, rather than a pleasant surprise, it turned out to be a rude shock for the couple. And to add insult to injury, their marriage has been rendered invalid by the courts. Oh lawd. More here.