This research has been correlational which means that happiness and conservatism covary, when one increases, the other increases. Correlational studies do not demonstrate causality. If A is related to B, if they are correlated, then A might cause B, or B might cause A, or some unknown factor X might cause them both.
The program took the view that being conservative made one happier, while being liberal made one less happy. What if the reverse were true? What if being happy made one more conservative and being unhappy made one progressive or interested in change.
I think this latter notion is much more reasonable. Happy people see change as a threat to their happy status quo, and become conservative - anti-change. Unhappy people see change as an opportunity to become happier and blame the unhappy status quo for their gloom.