Then why are the roofs so steep? Could be building material: can a small island lacking bodies of water even have clay, for roof tiles? A thatched roof would be impractical for harvesting rainfall. And when you go limestone masonry (apparently the building material available), you'll likely end up with something steep. Steep and stepped, unless you go the extra mile chiseling for smoothness. So the original cause for the stepped nature of the roofs is kind of related to water harvesting (even if the hurricanes mentioned in passing have likely been just as motivational against organic materials), and the steps might actually help by preventing high inertia of water hitting the gutter, but I suspect that's more a convenient coincidence than the accrual reason.
The same kind of steps were used even for catchment areas that weren't on houses. I remember passing (on the bus) an area that had a whole hill set up with the same kind of stepped/terraced limestone that fed down into some sort of reservoir.
Regarding the landscape catchment, if it's not in-situ stone that is laid bare and chiseled into shape it might simply be an economy of scale thing, use roofing commodity instead of reinventing the wheel. And if it's in-situ limestone, a major contributor to the decision for stepped/terraced might still be ease of maintenance access. The chemical qualities seem more like a convenient coincidence to me. Perhaps an enabling quality in absence of which they'd have long switched to desalination, but even that would not make it a causal "why". Particularly the part about UV working better with the reflections white making photons pass twice seems doubtful to me, because nighttime rain is probably not entirely unheard of (yeah, I might be wrong about this)