I'm curious to see how they surveyed for "happiness". As a parent the initial years are rough just providing care. In the thick of it if someone comes and asks, "are you happy?", the answer is irrelevant (I understand that the question won't be as direct, but the outcome will be similar). IMHO the best question is, "if you could go back in time would you still decide to have children?".
No way you'd get a straight answer to that since it's way, way too close to "do you wish your kids were dead?" It'd probably be tough to come up with any question that probes that sentiment that wouldn't be strongly affected by that problem.
My answer would be "go back in time and decide to have these children? 100% yes, no reservations. Go back in time but no guarantee (or even likelihood) that the kids will be the same? Probably would not want kids." Maybe shifting the question to focus in the direction of that second part would help, though I doubt it'd be enough to make it useful.