No one, not then-general manager Bill Polian, coach Marv Levy or chief scout John Butler, questioned the running back's potential after Thomas enjoyed a stellar four-year career at Oklahoma State.
There was plenty of concern, though, regarding the strength of Thomas' surgically repaired left knee, which he hurt before his junior season. The injury was the reason Thomas was still available when the Bills made their first pick, 40th overall - all but three teams passed on him, including the Raiders three times.
Wilson then provided a memorable response: "Hey, life's a gamble. Go ahead."
On Saturday, Thomas becomes the fourth member of that Bills team to be enshrined in the hall in Canton, Ohio, joining Levy, quarterback Jim Kelly and receiver James Lofton.
"When you draw the picture of the 1990s Bills, it wouldn't be complete until you paint him into it," said Levy, who will make the speech presenting Thomas at the induction ceremony.
Thomas chuckles at his fortune, knowing the injury might have been the best thing that ever happened.
"I always think back, had I not hurt my knee in college, I probably would've played fewer years and been on a horrible team," Thomas said. "I probably wouldn't have had the success I had with Buffalo."
Thomas spent the next 12 years with the Bills and added another with Miami before retiring after the 2000 season. The NFL's MVP in 1991 and a five-time Pro Bowl selection, he holds seven Bills records and still ranks 12th in the league with 12,074 career yards rushing, and eighth with 16,532 career yards from scrimmage.
He had a strong and keenly balanced running style, was a solid blocker and emerged as a more than capable receiver - something that came as a surprise, coming out of Oklahoma State's run-oriented system.
His added pass-catching dimension became a staple of the Bills' "K-Gun" no-huddle attack, and allowed Thomas to become the third running back, behind Walter Payton and Marcus Allen, to register 400 receptions and 10,000 yards rushing.
"I know why I'm in the Hall of Fame. No. 34 had a lot to do with it," Kelly said, referring to Thomas' jersey number. "One thing about Thurman, he never made that mental mistake. If he was supposed to pick up that linebacker, he was there. He was the full package. And that's what a quarterback like I needed all the time."
Not that Kelly and Thomas didn't have their differences. The team earned the nickname "The Bickering Bills" in 1989, when Thomas publicly criticized Kelly after the quarterback questioned a teammate.
Thomas acknowledged he could've handled the situation better, but noted it had a way of bonding the team after he and Kelly patched things up.
"I talked to Jim and said, `Hey, you know, we're a team ... we have to pull together and try to get this going,"' Thomas said. "I think the relationship got even stronger."
"People can say what they want to say," Thomas said. "We put Buffalo on the map. Whether you want to label us as losers or winners or what have you, there have been a lot of other teams that have never been to the Super Bowl."
Thomas plans to ask fellow 2007 inductee Michael Irvin how the Hall of Fame honor compares to winning a title; Irvin won three with Dallas.
"I wish I could've won a Super Bowl so I could feel what that felt like," Thomas said. "But if it's anything like this, I don't think there's anything you can compare it to."
Thomas enjoyed his breakout season in his second year, when he finished with 1,244 yards rushing and six touchdowns, and scored six more with 669 yards receiving. It marked the start of an eight-year run in which he broke 1,000 yards rushing.
Thomas also shone in the playoffs. He set an NFL postseason record by scoring touchdowns in nine straight games, and is tied for second, with Emmitt Smith, with 21 career playoff TDs.
If Thomas thought he was fortunate to wind up in Buffalo, the Bills couldn't believe their luck either.
"You stop to think back, if we had a first-round draft choice, we probably wouldn't have Thurman Thomas," Levy said. "So, sometimes what doesn't look so encouraging at first works out."
AP Sports Writer Michael Marot in Terre Haute, Ind., contributed this report.