The coraline in my tank does not mind water flow. It even grows on the powerheads to the point of needing 6 month vinegar washes.
When I had a FOWLR
and a single T8 bulb, the only coraline that lasted and grew was on the topside of the uppermost rocks. If yours is dying in areas where there is less light, then I would still suspect lights.
As for not needing specific lighting in a FOWLR
tank, it's true because caoraline algae is not critical or even important to the health of the tank. I thinks its purely asthetic.