To be specific, the regression models they use assume no measurement error in predictors. In this case BMI isn't even a direct measure of adiposity, so it's kin

To be specific, the regression models they use assume no measurement error in predictors. In this case BMI isn't even a direct measure of adiposity, so it's kind of obvious, but even if they had a direct measure of body fat the issue could remain because error in measurement of predictors would attenuate the ability of this covariate to eliminate confounding.