"The last thing I wanted to do, is to be that person," Woods said with tears during an appearance on "Red Table Talk" aired on Friday. "I am not a house destroyer."
The model is at the center of a cheating scandal involving long-time reality star Khloe Kardashian and Thompson, who is the father of Khardashian's granddaughter and a professional basketball player.
The situation as a whole was further complicated by the fact that Woods is Kardashian's younger sister's best friend, makeup naïve Kylie Jenner, for a decade.
On Friday, Woods appeared on Facebook on "Red Table Talk" by Jada Pinkett Smith.
It was explained that Pinkett Smith and her husband, the movie star Will Smith, had known Woods all his life, his father being the sound engineer of Smith's famous TV show, "The Prince of Bel Air," and families have become friends.
It's their son, rapper / singer Jaden Smith, who introduced Woods to Jenner, said Pinkett Smith. The controversy has affected all families.
Smith, who films "Bad Boys III", called before the siege to offer his support to Woods.
"I want you to know that you are supported," he said. "I have you and we have you."
"This world is not going to break you," he added. "We will not allow it."
"There is a family who feels betrayed by you," Pinkett Smith told Woods early in their conversation. "I want to give you the opportunity to tell your truth and I want you to say it through the purpose of your role, because that's the only thing you can change."
According to Woods, she and a few others went back to Thompson after dinner and had a drink in a bar where they met.
Woods said that she did not think "what I would feel if a person close to me was hanging around my ex or my child's father" and said that it was bad judgment on his part.
She also said that Thompson had kissed her, without passion, as she was leaving.
"It was a kiss on the lips, no kissing of the tongue, no making head," she says. "I do not think he's wrong either because I allowed myself to be in that position."
But she denied reports that she gave Thompson a lap dance or that the couple became intimate.
"I should have gone home after the evening, I should not have been there," Woods said. "I never did him a dance tour, I sat on him … I never left him to go out of the public area, to go to a bedroom."
Kardashian did not seem to buy the story.
She tweeted "Why are you lying @jordynwoods?"
"If you are trying to save your skin by becoming public, you must at least be honest with your story," Khardashian tweeted. "BTW, you're the reason my family broke up!"
She also tweeted about Thompson, who made the headlines being spotted by another woman a few days before Kardashian 's birth last year.
"Tristan is also to blame but Tristan is the father of my child, no matter what he does to me, I will not do that to my daughter," Kardashian said on Twitter. "He approached this situation privately, if Tristan was publicly lying about what had plotted, then yes, I would talk to him publicly too."
On Tuesday, Kardashian tweeted: "Hi loves, I wanted you to know I appreciate you!"
"I have read your kind words and they are truly a blessing to me," wrote Kardashian. "I love you! Thank you Thank you! I'll be back when I'll be in the mood to chat with you all. Until then, remember to be kind to each other."
CNN asked Woods, Kardashian and Thompson for additional comments.