On average people with kids would rate their happiness lower, but when these people are asked whether having kids made them happier they would say yes.
So are they happier? Not sure. Could be exactly as you say, but in one sense that bug may actually mean they are truly happier.
This can be quite easily explained by peer pressure - You are expected to treat children as precious little gifts from god, and speaking ill about them makes you look bad in the eyes of your peers.
That being said I have also (fewer) close friends who have told me they are less happy. So you have a point.
The fact is, you will encounter plenty of misery in life regardless. You should not choose based on what makes you happy, but arguably based on what kinds of misery you are more suited to - the misery of having children or the misery of not having children.
It's as if having kids rewrote the utility function of the person, introducing a bug to pass the test suite ("self satisfaction") to allow for a wider diffusion of the behavior ("I'm so much happier now, trust me it's wonderful!"), yet in a flawed way (i.e. that's not robust to scientific inquiry, as you observed)