It's been proven before; as they said, they reviewed the literature. They're not the first to test this theory, but hopefully they are the last.
I tend to think a lot of it is in the pitch. Everyone knows about how abrasive conditions lead to reverse swing, but the opposite is true of conventional swing; there are some pitches that just don't look like they'll see a lot of swing. A good surface for swing bowling is not necessarily green, but is very gentle on the ball. It's been noted at the WACA in recent times that the ball leaves visible marks on the pitch; so it's reasonable to assume the ball is in newish condition for longer.
And while there was never a clear link as to how humidity ought to affect the ball, the water content of clay does change with humidity. A cricket pitch that contains moisture is unlikely to dry out quickly in humid air.
However, what ought to satisfy pundits is the theory they put forward about overcast conditions reducing turbulence. From this we can also predict that reverse swing, where the laminar airflow around the ball needs to be entirely turbulent, should occur more readily in hot, sunny conditions.