But with the news Thursday that both Ortiz and Ramirez tested positive for performance-enhancing drugs in 2003 under Major League Baseball's survey program, according to a New York Times report, Damon cannot be sure if the celebrations of that "curse-reversing" season are now tainted.
"That probably is what's being said, and that's what makes guys like me upset," Damon said. "I was never in that conversation with guys who said when and where they would do it. It wasn't in lockers. That's the tough thing. I've never been in that conversation."
Yankees third baseman Alex Rodriguez, who was named as one of the 104 players on that list this spring and later admitted to using performance-enhancing drugs from 2001-03, had few words to offer on the subject.
"He's my friend, and I care for David," Rodriguez said. "I have nothing else to say about it."
But both Damon and Mark Teixeira had plenty to offer, opining that they would be in favor of releasing the full list of 104 players who are on that list with Ortiz, Ramirez and Rodriguez.
Damon said that he is tired of holding court with reporters on the subject and believes the Players Association sympathizes with the position.
"I think they know how we feel," Damon said. "This has to end so we can concentrate on playing baseball. It's real tough, because you're dealing with someone who's working on the inside who claims to be a source.
"We need to find out who that person is, too, I think. These names keep coming out, and I'm sure the other 97 guys are probably thinking they're going to come out also."
Teixeira, who was a Rangers rookie in 2003, said that he still does not understand how what was intended to be an anonymous testing program could have become public. But now that it is, Teixeira said it would be best if the results would not trickle out unpredictably.
"Names are going to keep coming out," Teixeira said. "I agree with everyone else who says just put it all out. It's ridiculous. Just let all the games go out and let everyone deal with it at the same time.
"Every two months, things come out, and it's not good for the game. It happened in 2003. Let it all come out, let everyone talk about it for one or two days, and then we can move on."
Yankees shortstop Derek Jeter said that he is also weary of the topic popping up periodically, but he said he was not sure that releasing the 2003 list would help matters. Jeter's concern is making the point that not everyone was using performance-enhancing drugs during that time period.
"I'll stick to what I said before," Jeter said. "Not everyone was doing it. You're talking about 100 people. There's a lot more than 100 people playing baseball. It's unfortunate that we have to sit here and talk about another name a couple of months later. I wish that wasn't the case."
Yankees manager Joe Girardi said that it pains him to see the game he loves continue to have to battle with the years-old results of that survey program, while wondering how much damage was done to baseball's hallowed statistical records during that time.
"It's like ripping a Band-Aid off slowly," Girardi said. "It's unfortunate, because we're trying to get this era beyond us and repair the game. The names keep coming out. It just seems to make it more difficult and last longer."
But it is believed that the current Major League testing program has paid dividends and cleaned up the game markedly.
Damon said he had been "saddened" when Ramirez was hit with a 50-game suspension earlier this season, but said that -- by and large -- players have been playing by the rules and operating on a level playing field.
"Hopefully, one day all this will be past, and the players who did cheat the game in some way won't be playing anymore," Damon said.
On that note, Teixeira said that he is proud he can look at his statistical achievements without wondering if he will appear on any future lists, though he made certain to note that he does not pass judgment on any past players.
"As a guy who has done things the right way their entire career, I don't want any kid looking at me saying, 'Whoa, did you do something? Were you on a list?'" Teixeira said.
"I look at my generation and players like myself, Matt Holliday, Chase Utley. These guys are doing it from 2003 on and doing it the right way. I want kids to look at us and say, 'These guys are great players without using that stuff.'"
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.