They say they controlled for BMI, but if the dependence on BMI is nonlinear (i.e. higher BMI reinforces it's own destructive effect on testosterone) then there

They say they controlled for BMI, but if the dependence on BMI is nonlinear (i.e. higher BMI reinforces it's own destructive effect on testosterone) then there will still be a residual effect after that control. I think this effect is entirely due to BMI.