When I asked the same of Jones, his response was somewhat less clear. “Oh, boy,” he kept saying. “Boy. Boy! Boy! Boy! Boy.” We were sitting aboard the Dallas Cowboys’ bus in the parking lot of a golf course not far from the Dallas-Fort Worth International Airport. As a general rule, the Dallas Cowboys’ bus is not a place for the faint of heart or liver.

“I do like to have a drink,” Jones confirmed, something I’d heard from a few people. “Do you want a shot of Scotch?” he asked me. Sure, I said, not realizing that by “shot,” Jones was talking about large blue plastic souvenir cups bearing the Cowboys’ logo, soon to be filled (and refilled) with Johnnie Walker Blue Label, Jones’s favored libation.

I relay this by way of transparency into Jones’s inhibitions, which were relaxing rapidly. When I asked him again whether he would trade his gold jacket for another ring, Jerry’s face assumed a kind of happy grimace at this high-class dilemma. Finally, he answered. “No,” he said.

Sitting a few feet away, Rich Dalrymple, the Cowboys’ longtime head of public relations, shook his head. “You messed that one up,” he told his boss. Dalrymple wanted Jones to amend his answer to “another Super Bowl ring.” That would reassure fans that nothing was more important to their owner than winning another championship more than 20 years after the last one. Otherwise, it’s just a rich guy’s ego trip (which it is, of course, but you’re supposed to hide it better).

Some of Jones’s fellow owners have described him as the N.F.L.’s Donald Trump, a blustering billionaire showman easily dismissed as a carnival barker. When I asked Jones how he felt about this, he was thrilled. Trump’s rise, he said, “is one of the great stories in America. And let me tell you this,” he went on, “the president ain’t no joke. He’s got as good a chance to be right as any of them.”

Several N.F.L. owners had known Trump for years, with Kraft being his highest-profile friend among them. (Kraft has given him a Super Bowl ring.) But Kraft, too, is a politician, of sorts, who seems to do his best to please as many audiences as he can; in part through having mastered the art of saying quite different things for public and private consumption. His friendship with Trump provides a case in point. Kraft loves being a presidential buddy but is also aware that many of his plutocrat friends don’t approve. So Kraft is quick to mention to his friends — privately — that he disagrees with Trump on many issues and with many of the incendiary things the president has done and said. But he would rather have the presidential ear and try to be a positive influence. Arthur Blank, the Falcons owner, told me that Kraft tried to sell him on this line, but he wasn’t buying. “I said, ‘You [expletive], you’ve given him a lot of money,’ ” Blank told his friend Kraft (who disputes parts of Blank’s account of their conversation). Blank’s own line on Trump, which he says he also told Kraft, is that “there are things he’s saying and doing that are not great for this country.”

The N.F.L. has long possessed the charmed ability, or luck, to fold even its most embarrassing fiascos into its blockbuster reality show. I remember thinking as much when Tom Brady’s Deflategate news conference was being carried live all over cable and leading all the news shows. What started out as a scandal quickly became an engrossing story line and a pleasing snack food following a season dominated by the heavy indigestion of Ray Rice and domestic violence.