Bill Parcells left the Patriots in large part because owner Robert Kraft sided with Grier, the vice president of player personnel, on the selection of Ohio State receiver Terry Glenn in 1996. The rift led to Parcells' infamous "buy the groceries" comment.
Bill Belichick fired Grier in May 2000 to install his vision of the front office.
Two weeks before Belichick dumped him, however, Grier played a role in helping the Patriots draft their greatest player.
ESPN's documentary, "The Brady 6," will debut Tuesday night. The hour-long film looks back at how Tom Brady went from the 199th draft choice to a first-ballot Hall of Famer, while the six quarterbacks taken ahead of him didn't come close to measuring up.
One of the more surprising revelations comes from Lloyd Carr, Brady's head coach at Michigan.
Bobby Grier was the only NFL executive who contacted Lloyd Carr about Tom Brady.
With scouts presumably examining all imaginable minutia while grading prospects -- the Carolina Panthers reportedly have requested Cam Newton game film from Blinn Junior College -- only one NFL executive contacted Carr about Brady.
"Bobby Grier, who was with the Patriots at the time, talked about they were going to draft a quarterback late," Carr said in the documentary. "I just said, 'Bobby, I guarantee you you'll never regret drafting Tom Brady.'"
Dick Rehbein, the late quarterbacks coach, gets a lot of credit for Brady ending up with New England. Rehbein's glowing report of a Brady workout in Michigan was significant. But Grier apparently was the lone NFL executive to check with the coach who knew Brady best.
The Patriots were hesitant to draft Brady because of circumstances that caused the Wolverines to force Drew Henson onto the field. But that had more to do with trying to keep Henson from playing baseball than feeling Brady wasn't good enough.
"One of the real troubling parts was the Michigan situation -- the fact that, really, they were trying to replace him as their starting quarterback," Belichick said in the film. "You say, 'OK, they don't really want this guy as their starting quarterback. They want another guy. What's the problem here?' It was a little bit of a red flag there."
Grier's call to Carr was wise to find out the true story of what transpired at Michigan.
In the Buffalo Sabres' locker room at HSBC Arena (of all places), I had a chance Monday to ask one of Grier's sons about the Brady pick. Mike Grier is a Sabres forward getting ready to play the Philadelphia Flyers in the first round of the NHL playoffs.
"He deserves a lot of credit," Mike Grier said. "He was always doing everything he could, never left any stone unturned when evaluating players. As a kid growing up, he was always coming in the door at 10 or 11 o'clock at night. He was spending all those hours in the office. I know he put in the time and cared about what he was doing."
Mike Grier said his father is too reserved to revel in his successful moves. But Grier's sons can read him and are knowledgeable enough about sports to figure it out for themselves. Chris Grier is the Miami Dolphins' director of college scouting.
"He'll never let me or anyone else know about it or talk about it," Mike Grier said, "but just being around him and talking with my brother, I know that he's pretty proud of that draft class and Tom in particular.
"He did his homework, and for me personally, it's something every time Tom does something and plays the way he does, it puts a smile on my face the way things ended for my dad there in New England. But I think he did a pretty good job. I'm very proud of him for what he did there."
Mike Grier grew up a Patriots fan. He was born in Detroit while his father was running backs coach at Eastern Michigan. The family moved to Massachusetts when Grier took a job at Boston College in 1978 and joined the Patriots three years later.
Mike Grier starred on the ice for St. Sebastian's School in Needham, Mass., and then Boston University. He was an All-American and finalist for the 1995 Hobey Baker Award, college hockey's version of the Heisman Trophy.
But Mike Grier can't root for the Patriots anymore, not given his dad's departure and his brother's role with the AFC East rival Dolphins.
"It's hard for me," Mike Grier said with a laugh. "I grew up hating those guys. But I root for them every Sunday."
So what does a Dolphins fan with connections to the front office think they'll do with the 15th pick?
"I don't know," Mike Grier said. "But I'd like to see them get a quarterback or a running back."