The entire market of SAD lights was fluorescents pre-LEDs, they can be made just as "full spectrum" as LEDs are (by which I mean neither is capable of true full spectrum, just an approximation with appropriate phosphors).
Yeah, I assumed you were saying that the physiatrist was insisting on the use of incandescents for that reason. I don't know why someone would interpret you as saying that LEDs were superior to fluorescents, since obviously neither one produces full-spectrum light!