This, Braden vehemently contended, was a violation of one of baseball's unwritten rules. "He should probably take a note from his captain [Derek Jeter] over there and realize you don't cross the pitcher's mound in between an inning or during the game. I was just dumbfounded that he would let that slip his mind -- being someone of such status.
"I don't care if I'm Cy Young or the 25th man on the roster, if I've got the ball in my hand and I'm on that mound, that's my mound. ... He ran across the pitcher's mound, foot on my rubber. No, not happening. We're not the doormat anymore."
Rodriguez responded by saying: "He just told me to get off his mound. I was a little surprised. I'd never quite heard that. Especially from a guy that has a handful of wins in his career. ... I thought it was pretty funny, actually."
There had been additional verbiage back and forth in the interim, but, after Sunday, nobody could refer to Braden as a pitcher known only for having a controversy with a superstar. His perfect game was just the 19th in Major League history.
The perfect game finished just as the Yankees were to begin batting practice at Fenway Park for their Sunday night game against the Boston Red Sox. Rodriguez addressed this development in a very brief but still gracious statement to reporters.
"I've learned in my career that it's always better to be recognized for some of the great things you do on the field," A-Rod said. "Good for him. He threw a perfect game, and even better, he beat the Rays."
Coincidentally, Yankees manager Joe Girardi was reaching the end of his daily pregame session with the media when news came that Braden was two outs away from the perfect game. Girardi was extremely gracious in wishing success to Braden.
"I hope he gets it," Girardi said of the perfect game. "I don't have any hard feelings toward Dallas Braden. I hope he gets it. God bless him."
Earlier in the series, Girardi had declined to comment on the Braden-Rodriguez controversy, pointing out that the Yankees did not play the Athletics again until July and noting that all his managerial attention was focused on the series against the arch-rival Red Sox.
But Girardi was happy enough to wish Braden well on the occasion of what was then a near-perfect game. When it was suggested to Girardi that he was pulling for Braden because Braden was pitching against the Rays, who were a half-game ahead of the Yankees going into Sunday.
The manager smiled and responded: "That always helps -- a team within our division."
So it could be argued that Braden did the Yankees a favor on Sunday, taking some of the luster off the terrific start Tampa Bay has had to the 2010 season, giving New York a helping hand in the American League East standings.
But he did himself a larger favor. The name Dallas Braden will no longer be primarily connected to the notion that "he was the guy who didn't want A-Rod on his mound."
For now and all the times to come in which baseball is played, Braden will be known as a man who threw a perfect game. As even Rodriguez said: "Good for him."