Grey's Anatomy star apologizes for gay slur

Well, it's about time.

Grey's Anatomy actor Isaiah Washington has finally issued an apologyf or his behavior during an on-set argument with costar Patrick Dempsey. After Washington and Dempsey, 40, clashed on Oct. 9, reports surfaced that Washington had used a homophobic slur during the fracas. Then on Oct. 19, their costar T.R. Knight disclosed to PEOPLE that he is gay.

In an exclusive statement to PEOPLE, the same venue Knight used to make his announcement, Washington said:
"I sincerely regret my actions and the unfortunate use of words during the recent incident on-set. Both are beneath my own personal standards. … I have nothing but respect for my coworkers … and have apologized personally to everyone involved."

There had been reports that Washington's job was in jeopardy and that be might be replaced by former ER star Eriq La Salle. Show creator Shonda Rhimes, who has put together one of the most racially diverse casts of any show ever on television, told PEOPLE that Washington was not being fired or replaced.

"I found (those rumors) not only ridiculous but offensive that we would consider replacing a member of our family," Rhimes says. "And also the (idea) that one black man was interchangeable with another seemed disturbing to me...We have a group of people who are more of a family than anything else. We have our fun days, and we have our days when people are tired and the work is hard."

On Tuesday's episode of The Ellen DeGeneres Show, Grey's costar Katherine Heigl played down the incident, calling it "some scuffle … There was a little burst of testosterone in the room, and then within five minutes ... they were totally fine." So what actually happened between Washington and Dempsey? A set source says that when Knight, 33, was late to film a scene, a debate ensued between Dempsey and Washington, with Dempsey insisting on waiting for Knight before starting the scene. The argument quickly intensified, and the source says that yes, the alleged slur was used, but Knight was not present at the time.

"Isaiah was running his mouth off," says the source. "Isaiah verbally attacked Patrick – he tore into him. Patrick's voice escalated and he did tell Isaiah to 'f– off, (but) that was as heated as Patrick got."

Rhimes tells PEOPLE that Dempsey and Washington "are fine" – as are Washington and Knight. "They've had conversations," she says. "They did a really great scene together the other day." The whole affair, she says, "was four and a half seconds of one day in three years. I feel like we've already moved on."