I have to wonder if the researchers have the famous "causal arrow" pointing in the right direction. That is, what if having parents with negative mental health causes some children to have problems instead of vice versa?
Technical note: if it is a correlational study, as it appears to be, X can influence Y or Y can influence X when the two are found to be correlated. For completeness sake, I should add that some third force, Z, might influence both.