He said Thompson was sure she had identified the right man.
Cotton heard the news from his mother's boyfriend. "He told me. He said, 'Ron.' He said, 'The police are looking for you.' And I said, 'For what?' And he told me, 'For rape.' And I said, 'I haven't committed such a crime like that,'" Cotton recalled.
Asked if he panicked, Cotton told Stahl, "I didn't panic. I tried to figure out, you know, why."
"He comes in and gives me a very detailed account of where he was, who he was with that night. As it turns out, that was a false alibi," Gauldin said.
"I realized later that I had got my weekends confused, so therefore it gave them reason to think that I was lying," Cotton explained.
"This was August 1, 1984," Stahl remarked.
"Right," Cotton replied.
Cotton went to the police to clear his name, but he didn't get to leave. He was locked up, and days later put in a physical lineup.
"I'm number five," Cotton remembered. "I was very scared, nervous. I was so nervous, I was trembling. I felt my body just shaking."
Gauldin says the men in the lineup were asked to step forward, speak, and step back.
"I could remember looking to the detective and saying, 'It's between four and five. Can I have them do it again?'" Thompson remembered.
And then she knew - it was man number five, Ronald Cotton.
She told Stahl she was "absolutely certain" she had picked the right man.
"Did anybody say to you, 'Good job?'" Stahl asked.
"Well, what was said to me afterwards was, 'That's the same person you picked out in the photo lineup.' So, in my mind I thought, 'Bingo. I did it right.' I did it right," she said.
In a week-long trial, the jury heard about Cotton's faulty alibi, his clothing that matched Thompson description, and a piece of foam found on her floor that seemed to come from one of his shoes.
And most powerfully, they heard from Thompson. In court, when asked if she recognized her rapist, she named Ronald Cotton.
"She called my name, pointed a finger. And that's all, that's all it takes, it seemed like," Cotton remembered.
Asked what that felt like, Cotton told Stahl, "It felt like someone pushing a knife through me."
It took the jury just 40 minutes to reach a verdict: guilty on all counts.
"He was sentenced to life and 50 years. And it was for me that moment that you know the justice system works. Because I am the victim, and he's a horrible person, and he will never, ever be free again," Thompson told Stahl.
Ronald Cotton was handcuffed, shackled, and taken to North Carolina's Central Prison. He was 22 years old.
"You know they say grown men doesn't cry, but it's a lie you know. I grabbed my pillow many times and hugged it, wishing I was hugging my mom, my dad, sister, brother. Wish it didn't have to be this way," Cotton told Stahl.
He started working in the prison kitchen, singing in the choir, and writing letter after letter to his attorneys, hoping to get a new trial. Then one day as he watched a new inmate being brought in, he had a strange feeling.
"I said, 'Excuse me.' I said, 'You look familiar.' I said, 'Where are you from?'' He said, 'I'm from Burlington.' I said, 'I am too.' I said, 'You kind of resembling the drawing of a suspect in a crime in which I'm falsely imprisoned for. Did you commit this crime?' And he told me, no, he did not," Cotton remembered.
Cotton said he thought of the composite drawing when he saw the inmate.
His name was Bobby Poole, and he was in for rape. He started working in the prison kitchen too.
"The stewards were calling me Poole instead of Cotton," Cotton said.
People were mistaking the two men.
Then a fellow inmate told him he'd heard Bobby Poole admit to raping Jennifer Thompson and the other woman that night. Ronald Cotton won a new trial and his lawyers called Bobby Poole to the stand with Thompson sitting right there. It was the moment Cotton had been hoping for.
"Bobby Poole is in the courtroom. You look over there. What happens inside you?" Stahl asked.
"Nothing," Thompson replied. "As a matter of fact, the strongest emotion I felt was anger at the defense because I thought, 'How dare you. How dare you question me? How dare you try to paint me as someone who could possibly have forgotten what my rapist looked like, I mean, the one person you would never forget. How dare you.'"
Ronald Cotton was convicted again, this time given two life sentences.