This woman is apparently not educated enough to know that correlation is not causation. Homosexual couples are not less healthy because they cannot marry. They are less healthy because their lifestyle is a less healthy way to live.
In this study, there isn't even a correlation. The lead researcher catalogued some health problems with homosexuals, and proposed that the underlying reason is the lack of marriage--a hypothesis that isn't even suggested by the data.
Her "methodology" seems very similar to the "methodology" of "global warming." Real phenomena are documented, real problems are discussed, but then everything is dismissed with the statement "caused by global warming."
As a scientist, I find this "methodology" extremely annoying in any context. It's not science. It's an attempt to coat a political belief with a veneer of science to give it credibility.