I went to see Boris with a friend, and in the evening after the opera she called to let me know that the plot was true. Boris and the false Dimitri were real. Dimitri became tsar but was assassinated by Shuisky who then became tsar. Then she called again to report that the real Boris did not kill Dimitri.
According to Wikipedia, Dimitri was illegitimate and ineligible to become tsar. They are vague about whether or not Boris killed him.
The opera is based on a play by Pushkin.