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The movie, which has shown at the festival to standing ovations, is a powerful work that its distributor Fox Searchlight has high hopes come the Oscars.
However, in the past month Parker has had to address a decade-old rape allegation, and a recent revelation that the alleged victim committed suicide in 2012. The story has taken over the success the film has had at festivals since sweeping the major awards at the Sundance Film Festival earlier this year.
In the hopes to put the attention back on the movie, Parker refused to address the rape topic at Sunday's press conference.
When New York Times writer Cara Buckley asked Parker if he plans to apologize to his alleged victim and her family, Parker said he didn't want to "hijack" the press conference to talk about his personal life.
"I've addressed this a few times," said Parker. "This [press conference] is a forum for the film and for the other people sitting on this stage. I do not own it. It is not mine."
Mashable's Jeff Sneider then asked Parker if he believes there's a double standard in Hollywood on how white people charged with sexual misconduct are treated versus African-Americans. This stemming from Oscar contender this year, Casey Affleck, receiving little attention for his past harassment allegations.
Parker gave a similar answer he gave Buckley and did not address it.
During the press conference Parker, who along with being the film's writer and director also plays Turner in the movie, and his fellow cast mates spoke about the hopes that the movie will be a bridge to starting a conversation about issues of racism and sexual abuse (the character played by Gabrielle Union in the movie is raped, she has since spoken out about being raped as a teen). Parker also said that he still plans to travel the country with the film to churches and college campuses to talk about social issues leading up to its October 7 release.
However, Sunday's press conference has proven that whatever setting Parker is given to talk about his movie he cannot escape having to address his past.