Adults who could not honestly report a reasonably sounding current situation would be less likely to want to participate in such a survey. Also note that the comparison is between same-sex parents (mostly females; "...80% of the children have female parents....") and "population normative data." That's not heterosexual parents but the whole population.
It also sounds like a snapshot. How will the children fare over the long haul? How many of the children raised by homosexual men will grow up to have some of the common health consequences of homosexual anal intercourse, etc., HIV being just one of them? How much stock does society in general put in monogamous, exclusive relationships anymore? How long do these allegedly cohesive partnerships last?
If we are going to make public policy, we need more than snapshots; and we need to see the research to rule out bias (witting or not) questions and interpretations.
"Australian children with same-sex attracted parents score higher than population samples on a number of parent-reported measures of child health." Note that it says "parent-reported." The only way to be sure about such things is to verify the parents' reporting by accessing the children's medical and other family records and to have them undergo testing. That applies to so-called stigmatization. It too is self-reported, including the parents' opinion as to impact, association/correlation, and causation all subject to manipulation depending upon the questions asked and the wording.