Leyritz says that the story is true. It was the morning of Oct. 29, 1996 -- three days after the Yankees celebrated their championship over the Atlanta Braves. The teammates both overslept, and Leyritz told Jeter to meet him in the lobby of his apartment building at East 64th Street and 2nd Avenue.
Surveying the scene on the street, Leyritz said that they quickly realized Manhattan gridlock would not allow them to reach the Canyon of Heroes by vehicle.
"We walked out and told the cops, 'Look, we've got to get to the parade,'" Leyritz recalled. "They said, 'You're not going to get down on the street. The only way you're going to get down is the subway.'
"So they escorted us down to the subway; it was my wife, my 2-year-old, Derek and I. We got on the subway, and the best thing was when we got on, people looked at us and were like, 'Why are you guys on the subway?' I said, 'This is the only way to get there!'"
Leyritz said that they boarded at 59th Street and Lexington Avenue, then rode the 4 train all the way downtown to City Hall. The commuters on board probably noticed Leyritz's cowboy hat first, but attention quickly turned to Jeter, who would soon be named the American League's Rookie of the Year.
"They didn't bother us bad," Leyritz said. "They were doing chants and having fun with it. It was packed. People were used to seeing me on the subway, because I took it every day. I think he was a little nervous. It was an extra-long ride; we got delayed a few times because of train traffic.
"This was before he became Derek Jeter -- he was just starting to be that. His notoriety, people were more enamored then, not obsessed. I always say to Derek, 'Dude, you can't go out in public anymore.' Back then, they were embracing it more. It was really fun. We were part of the fans."
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.