Reports that Big Brother sought to control Stormy to achieve a specific outcome are also completely false.
Moore relayed the details of her chat with Daniels, telling the studio audience: "This is her side of the story".
Asked whether anyone else in the United States had paid Daniels not to appear on the show, Moore said she had told her it was "not about money".
"She says that, late last night, she was due to be on Celebrity Big Brother and there was a custody development involving her daughter in America - she is in the middle of a divorce".
A spokesperson for CBB did not deny a row with producers and said Daniels told the production team "hours" before the show was due to air that she did not want to participate as agreed "several months earlier".
According to reports, Stormy Daniels, the adult film actress who supposedly slept with Donald Trump shortly after his marriage to Melania Trump, dropped out of appearing on the British reality show after failing to come to an agreement with the show's producers.
Lawyer Michael Avenatti said Friday that Daniels argued with producers who attempted to "control her and produce a certain result".
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"And suddenly she thought, "I can't do [CBB]'".
On Friday, presenter Rylan Clark-Neal told viewers: "Five hours before the live show, Stormy informed us that she wished to simply appear on launch night and then leave".
Her departure has apparently left producers particularly red-faced as the Celebrity Big Brother launch show set had been created to reference the 39-year-old's alleged affair with the President. "What she wanted to do was sort that out".
Moore went on to say: "It has now become a legal situation". "She's feeling as though she's had the power taken away from her".
She alleged the cash was to stop her claiming she had an affair with Mr Trump in 2006.
Channel 5 has since released Daniels' VT for the new series in which she said: "I'm now involved in a huge media storm involving the United States president and it has been shown on every news outlet around the world and has drastically changed my life". The president denies the encounter.
Newsbeat has contacted Stormy Daniel's representatives for comment.
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