The 10-second video, posted online on Sunday, was shot on a bus chartered for a date night by the fraternity.
Students were seen and heard chanting in unison, using offensive language referring to black people and vowing never to admit them to the fraternity.
The video was taken on a bus going to an event at a country club. The person who recorded it has cooperated with the investigation, Boren said Tuesday ahead of a Board of Regents meeting.
A sorority that may have been involved in the date night, Tri Delta, said it was cooperating with the university's investigation. Its house on campus has not faced any sanctions.
The controversy played out on social media with an online fundraising campaign launched for a black cook who lost her job because of the closure of the house.
Another video made the rounds purportedly showing the fraternity's white house mother using a racial slur.
William Bruce James II, one of the few black members of the Oklahoma fraternity, who attended the university from 2001 to 2005, said the SAE house there has undergone a cultural change from when he was a student.
"The guys in that video are not my brothers," he told CNN. He said he never heard an inkling of the offending song when he was a student.
On Tuesday, one fraternity member seen on the video and the parents of another issued statements apologizing.
In a statement emailed by his father, Parker Rice said the incident "likely was fueled by alcohol," but "that's not an excuse." He said he was "deeply sorry" for the performance, calling it "wrong and reckless," `'a horrible mistake" and "a devastating lesson" for which he is "seeking guidance."
He said he withdrew from the university Monday and that threatening calls to his family prompted them to leave their North Dallas home.
The parents of Levi Pettit posted a statement online saying they were shocked by their son's actions, that he "made a horrible mistake, and will live with the consequences forever."
Also on Tuesday, Beauton Gilbow, the fraternity's house mother, issued a statement that addressed a second online video from 2013 that had surfaced, showing her repeating a racial slur against blacks as music plays in the background.Gilbow said she was singing along to a song. She said she was "heartbroken" by the portrayal that she was racist but understood how the video must appear in the context of the week's events.