"I was like, 'I'm not funny! I am a serious actor!'" she recalled. "And he said, 'No you're actually funny and I think you should pay attention to that.'"
"Did you have a sense that you were funny?" Cowan asked.
"Yeah, I did, but my family was funny. We always were. I mean, I liked making people laugh. It was such a source of survival for me as a kid, you know, to be a clown and make people laugh."
Survival because, she says, it helped her deal with her parents splitting up when she was just nine years old.
"How much do you think that shaped you, having your parents get divorced?" Cowan asked
"Everything," she replied. "I mean, honestly the best thing that came out of it was my sense of humor, because there were some pretty sad moments, as any kid from a divorce will tell you."
Born in Sherman Oaks, Calif., Aniston was actually raised in New York City, in an apartment filled with entertainment, starting with her father, John.
He's appeared almost continuously on TV since the 1960s, including a nearly three-decade-long run as Victor in "Days of Our Lives."
Anniston says her dad didn't want her to become an actress. "Uh-uh. No. No, no, no. He didn't want my heart to be broken. Maybe that was my rebellion - was, 'Oh, yeah? I'm going to do that then. I'm going to try to be an actress.'"
She was accepted into Manhattan's LaGuardia High School, a prestigious school of performing arts.
The library, she says, was not her favorite place. "I just wanted to be downstairs in the drama department," she said.
Back then, Aniston was a bit more "round," as she puts it. She had a love affair with mayonnaise and white bread sandwiches, she said, pouring over her yearbook photos. "That's mayonnaise sandwiches all over there!" she laughed. "That's hysterical."
She still enjoys a good order of French fries, however, at one of her favorite hang-outs -- a Jackson Hole restaurant on the Upper West Side where she worked as a waitress between auditions.
"If I would get a play, or off-Broadway this or that, they would always let me go, do my play, and then they'd always have a spot for me when I finished," she said.
When she turned 20, Aniston traded burgers for the beach, moving to L.A. where her life in TV began.
Her first sitcom was called "Molloy." It only lasted one season, as did her next role on "Ferris Beuller" -- another flash-in-the-TV-pan.
"You were getting all these pilots, though, that just never seemed to go past a couple of episodes," said Cowan.
"Didn't matter to me," Aniston said. "I mean, I was just working. I was excited to be working."
And then, of course, came "Friends" -- the role that made Aniston (and her hair) famous.
"Friends" was a cultural phenomenon. It made Aniston America's sweetheart, and a darling of the tabloids.
The paparazzi were even waiting outside our interview to grab shots of Aniston leaving.
"It just seems like you have to deal with it so much more than anybody I can think of, pretty much," said Cowan.
"Yeah. Just don't pay attention, best you can," she said. "There was a period where I was hell-bent on saying, 'That's not true, that's not right, that's not fair.' And now I just think you have to let it roll off your back and you realize, I think everyone knows it's all BS and, like, soap opera on paper."