People are born with illness and sin. I guess you can steer this argument into saying that in some form, illness is allways derived from sin(not neccesarily the person who is inflicted being the one who sinned to gain the illness,) but its going to be an equal argument to as of illness being derived from innocence.
This topic is a pure expression of generalization, but when it comes down to it, everything still has its case by case basis.