(CBS)

Vice President Joe Biden used Sunday's "60 Minutes" interview to dispel several rumors about his deliberations on launching a 2016 presidential run — including one that helped kick-start a new round of speculation earlier this summer.

Biden told CBS' Norah O'Donnell in the interview that his late son, Beau, who died this May at the age of 46, did not urge his father to run from his death bed.

Biden said his two sons, Beau and Hunter, have always been his closest advisers.

"Some people have written that, you know, Beau on his death bed said, 'Dad, you've got to run,' and, there was this sort of 'Hollywood moment' that — you know, nothing like that ever, ever happened," Biden said. "Beau from the time he was in his 30s — or actually his late 20s — he and Hunter were one of my two most reliable advisors. And, Beau all along thought that I should run and I could win."

"But," Biden added, "there was not what was sort of made out as kind of this Hollywood-esque thing that at the last minute Beau grabbed my hand and said, 'Dad, you've got to run, like, win one for the Gipper.' It wasn't anything like that."

Reports of that "Hollywood" moment first prominently surfaced in an early-August column from The New York Times' Maureen Dowd. Dowd reported that when Beau Biden "realized he wasn't going to make it," he asked his father to chat.

"Beau was losing his nouns and the right side of his face was partially paralyzed. But he had a mission: He tried to make his father promise to run, arguing that the White House should not revert to the Clintons and that the country would be better off with Biden values," Dowd wrote.

Dowd reported that Hunter Biden had also encouraged his father to run, telling him, "Dad, it's who you are."

In the end, Biden said he didn't run because he didn't think he had enough time to mount a credible challenge to Democratic front-runner Hillary Clinton. He said he "likes" Clinton, and he said a line he used on a recurring basis last week — that he didn't consider Republicans an "enemy" — wasn't a dig at something she said during the Democratic presidential debate.

"That wasn't directed at Hillary. That was a reference to Washington. All of Washington," Biden said.

He later added: "Well, she was smiling when she said the Republicans. And I don't take it as, that's her view. But I do know it's the view of many people. Like, for example, and I know [on] this statement there were two big articles ready to say, 'Why is Biden so naïve? These people are our enemy.' From serious people. They're not my enemy. I — how in God's name can we govern this country if we view the opposition as an enemy?"