"That kid ain't never going to get it," he said.
Roger Clemens felt the same way and confronted Schilling during an offseason weight-lifting session at the Astrodome.
"You're wasting a lot of talent," Clemens told him.
From there, the conversation went downhill. Schilling recounted that story and plenty more like it over the years. Looking back on it, his growth, both physically and emotionally, may not have been all that unusual. He was 21 years old when he made his debut in 1988, and if he still had some growing up to do, he would not have been the first.
Something eventually clicked with Schilling, and when you consider the entirety of his 20-season career, it actually did not take all that long. And when he got it, he got it like few others. He became a warrior in every positive sense of that word.
Schilling was the living, breathing definition of a No. 1 starter. That is, he was at his best when the lights were the brightest and the stakes the highest. He was 11-2 in the postseason, with a dazzling 2.23 ERA. He started seven times in the World Series and had a 2.06 ERA.
Maybe you heard Schilling pitched Game 6 of the 2004 American League Championship Series with an ankle that doctors crudely sewed up to get him back on the mound. He was pretty good in a lot of small games, too.
For some reason, I will always identify him with a game that was actually pretty awful. On July 3, 2001, he pitched a game at Minute Maid Park in which he had absolutely nothing in terms of stuff.
Schilling got hit early and often that night, allowing 16 baserunners and six earned runs in seven innings. Yet what he did that night spoke volumes about his transformation. Even with nothing, he gave the D-backs seven innings, because he felt it was his responsibility to get the game into the eighth inning and save the bullpen a bit and perhaps make things easier the next night.
Once when I asked Schilling if he remembered that night, he smiled.
"You know, in a lot of ways those are the games you really cherish, because you're out there battling, doing whatever you can to give your team a chance," he said. "When you go out there with great stuff, it's completely different."
Schilling's larger legacy will be those postseason games, and that he was a key member of three teams that won the World Series -- the 2001 D-backs and the '04 and '07 Red Sox. He will be remembered for pitching as many as 200 innings nine times in his career and at least 250 innings four times.
In 10 seasons between 1995 and 2004, he averaged 15 victories, 29 starts, 212 innings and 224 strikeouts. So, yeah, when that something clicked, it clicked in a big way.
Schilling's credentials say he belongs in the Hall of Fame, and it should not even be a difficult discussion. That his name was checked on just 29.2 percent of the 2014 ballots speaks, not to his qualifications, but to the huge knucklehead factor of the members of the Baseball Writers' Association of America who cast votes. The snub is irrelevant to the people who played with and faced him and to the people who covered him and know what he was about.
At 47, Schilling is about to begin another chapter of his life as one of ESPN's lead analysts on "Sunday Night Baseball." That chapter was put on hold Wednesday when Schilling released a statement that said he had received a diagnosis of cancer. He offered no details, saying only that he had been raised to confront challenges head on and that he would do so again this time.
That attitude is no surprise to the people who have come to know and admire Schilling. His tenacity and resolve could serve him well in this latest fight. Meanwhile, here is hoping he understands how many people are rooting for him and praying for him and can't wait to see him back at the ballpark.