"The greater amount of athletes do a tremendous amount of good things. They're not getting in trouble," Staubach said.
Renfro said that, now as then, players have to rely on their own good character to stay out of the headlines for the wrong reasons.
"You know that your every move and your every word is going to be recorded. And if your character is good enough, and you are a good enough person, you're not going to do those things that are going to bring attention to you that isn't good," Renfro said. "It's just a matter of keeping your nose clean. Some of these guys nowadays they think they're above the law and they really don't care."
"Of course, you have the good ones who are going to do the right thing," he said.
Staubach played only for the Cowboys, has been married to the same woman for 47 years and ended his career with a squeaky clean image. He said Monday he couldn't recall if he had done anything wrong while on the public stage.
"I don't know if there's anything that came out that I, I don't know, nothing overwhelming that I know of," he said. "Are you looking for something?"