"Grey's Anatomy" began with two surgeons vying for a promotion, and it appears that their has rivalry bled over to the real world.

Patrick Dempsey and Isaiah Washington -- who play Dr. Derek "McDreamy" Shepherd and Dr. Preston Burke, respectively -- got into an argument that nearly became physical on set Monday (Oct. 9), report various news sources.

"We were like two baseball players . . . nose-to-nose," Washington tells People. "We had a difference of opinions while working on set but we've resolved it." They were reportedly arguing about "time and [keeping] the production going. The communication was lost in translation."

Luckily, the services of plastic surgeon McSteamy weren't needed since it didn't come to blows.

"Our faces are too beautiful for that," says Washington, who observed after a script read-through, "I've never been that close to [Patrick] before. He has really pretty blue eyes."

This happy picture is a lot more benign than the account reported the NY Daily News' Rush & Molloy and the National Enquirer. That story has Washington grousing about having to wait around on set and then saying "something mean" to actor T.R. Knight ( who plays intern George) when Dempsey came to his co-star's defense. Washington then allegedly grabbed Dempsey by the throat and shoved him a few feet.

The tabloid's unidentified source says that the scuffle was a long time in coming since Washington is supposedly jealous of Dempsey's "McDreamy" magazine cover status.

"There was an argument on set. In any close-knit family, sometimes people argue," says Dempsey's rep. "But everybody made up and went back to work."