"Your job in that chair of scouting director is listen to your guys talk about the better players all throughout the country," Allison said. "And in pure athleticism, this kid was one of the best and he did like playing baseball."
Tate also liked playing football and had committed to playing for Notre Dame.
"We knew we were never going to get close to signing him, but sometimes things change," Allison said. "The scout did a good job fostering a relationship in case something had changed. So we selected him and watched a little bit in the summer and then it was time to go to football practice, and we never got close to signing him. We would have had to have had several things fall into place."
Tate starred immediately on the football field at Notre Dame, but as the D-backs noted, he really did like baseball and played baseball for the Fighting Irish during his freshman and sophomore years.
Tate would have a second chance at baseball when the Giants selected him in the 50th round of the 2010 First-Year Player Draft. That was just a couple of months after Tate was picked by the Seattle Seahawks in the second round of the NFL Draft.
Playing football certainly was the right decision for Tate, who led the Seahawks in receiving this season and figures to play a big role in Seattle's offense in Sunday's Super Bowl.
"I'll tell you, he's fun to watch on Sundays," said Allison, who is now the Mariners' director of pro scouting.
Had he chosen to go the baseball route, though, Tate certainly appeared to have the talent to make it to the big leagues.
While some football players like NFL running back Cedric Benson were able to play baseball on their raw athletic ability, Tate was more polished on the diamond, like his current NFL teammate, quarterback Russell Wilson.
"What his problem was is sharing the two sports, he got kind of bulky," Allison said. "He lost a little baseball flexibility. As you watch him play today on the football field, you see just pure determination and confidence that he had at that time that just kept him so locked in. He was certainly not raw."
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.