The economists' models of the world are notoriously flawed and dangerous precisely because they leave out non-easily-measurable results and consequences.
Modern statistical tools allow economists to ferret out the most obscure factors. They're remarkably good at this, although not infallible -- our continued poor understanding of macro issues is a glaring example, but the topics being discussed here are decidedly micro.
I think the real answer to your comment is that economic models are (frequently) far more pointed than people like to admit. When they're forced to confront the fact that their observed behavior doesn't match what they espouse, they prefer to shoot the messenger rather than admit that they're not practicing what they preach.
Did you read the article? It doesn't ferret out any obscure factors? It has people read an article and then make some statement. And even then it doesn't even compare against those who don't have kids, but wanted kids or a whole slew of other useful controls.
But more importantly read the headline to the article, "Does having kids make parents delusional" -- yet NONE of the tests were about that. The tests were "Does Pointing out the Benefits of Parenting Reduce Its Perceived Benefit". That's a totally different story.