While I was reading this article I felt almost the exact same thing - the whole article feels like bad science because they present the conclusion that "many scientists believe that genetic mutations that build up in the sperm of older men are to blame." Presumably, the only thing this study has shown is that lower intelligence is correlated with older fathers but the cause could be any number of factors like what you said or even, for example, that people with lower intelligences are predisposed to postpone having children.

Basically, thanks Freakonomics for bringing correlation/causation to my mind every time I read an article like this.