Letters to the Editor
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Parenting style is not the be all, end all of parental influence or behavior
First, whoever's writing the headlines...I really think the tactic of raising an alarmist and misandrist strawman (Is it all their dads' fault?) only to say, "oh, no, look, there's some ambiguity at the end of the tunnel...") is not only unnecessarily sensationalist...but is probably inviting a lot of the scorn in the letters section that probably wouldn't have been directed at the substance of the posting, except for the headline.
Second, just because the mothers' general "parenting styles" weren't shown to have an effect, does not mean that other aspects of their behavior don't have effects. Other studies (including one more recent than this, but I couldn't find it) have indeed shown links between mothers' dieting behavior and their daughters' ideas about their bodies:
http://findarticles.com/p/articles/mi_m0887/is_11_19/ai_76284033
It's interesting that fathers' parenting styles have greater effects on actual weight--truthfully, it's not what I would've guessed. But it's a long way from concluding what the headline makes us anticipate Carol's going to say. And it's that snazzy headline that gets remembered, not the rest of the article.