TV news sucks

[Paraphrasing] Story on NBC Nightly News: New study shows role of genes in obesity. This study compared the weight of children at six years of age to their mother's weight. It found that while there was no difference between birth weight for children with obese mothers and children with non-obese mothers, by age six children with overweight mothers were 15x more likely to be overweight.
Me: Wouldn't obese mothers feeding their children worse diets than non-obese mothers produce the same results? Couldn't be this checked by examining the children of overweight mothers who weren't raised by their birth mother? Hopefully, NBC just misstated the study and it actually does test the effect of genes on obesity.