Raveling, who also coached at Washington State and Iowa and was a commentator for Fox Sports Net, was on the podium with King as he delivered his famous "I have a dream" speech in front of 200,000 people at the Lincoln Memorial in 1963.
Raveling still has the original copy of the speech.
"He basically just went to go see the speech, and they said, 'Hey, kid, want to do security?'" Rivers said of Raveling.
Rivers said he speaks to his players every year about King and black history.
"When we've really made it as a country, it'll be called American history, in my opinion," Rivers said.
The Clippers, who beat the Boston Celtics 102-93 on Monday, said it was an honor to be able to play on Martin Luther King Jr. day.
"It's big," Chris Paul said. "A lot of us look at making it to the NBA and being so successful, and sometimes you lose sight of how we even got here in the first place -- so it's always special to play on Martin Luther King Day. It's crazy for me now being a father and teaching my son. He was at home yesterday talking about what today is. It means a lot."
Blake Griffin added that King was an inspiration to him because of the way he fought for equal rights.
"A guy like that who fought for so much, but fought in the right way, stood for the right things," Griffin said of King. "He did it without violence. He did it in the right way, in the smart way. It's important to keep the dream alive and to educate the young people to keep the dream alive."