The reason this worked is, that the back-action of the moon on the sun is very insignificant. For a "real" chaotic three-body system, you need three bodies that interact with each other on comparable scales.
From the artcile: "The numbers were small — 13 metformin-exposed boys were born with genital defects. But after the researchers adjusted for factors including parental ages and maternal smoking status, they found a 3.39-fold rise in the odds of a genital defect. “The rate per se was surprisingly high,” Wensink says."