The case was over a story that the National Enquirer last year that implied Hudson had an eating disorder, the Southampton Press-Gazette reported Thursday.
The court was told that on Oct. 24 of last year, the tabloid magazine published a two-page story under the headline "Goldie tells Kate: Eat Something and she Listens! - Star confronts daughter after photos showing her painfully thin."
Hudson's lawyer, Simon Smith, said, "The article accused the claimant of being 'way too thin' asserting that her weight had dropped to a 'dangerous level', and that she was 'looking like skin and bones'."
"The allegations are entirely false and were deeply offensive and embarrassing to the claimant," he added.
The Enquirer's publisher, American Media, settled the case by publishing an apology, and made a statement in court apologizing for the "deep distress and acute embarrassment caused".
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