You are both correct. To a degree. When means actually, you are both incorrect. So there.
When plants die they form what we call organic material — fertilizer. As swards of grasses were cultivated and nurtured by man the process began to feed on itself. As turfgrass dies — and about 1/3 of the plant dies per year — it leaves in its wake this needed material. This happening fosters more growth in areas with less fertilizer (organic material) as the wind and water carries this "free" organic material from area to area. The footsteps of man, animals, rivlets of water, wind, mix of sand, etc., are all factors.
The best soils to grow turfgrass are sand-based. Today we greatly accelerate the process — adding organics (just the right amount) at the beginning and, of course, adding water nd fertilizer as needed.
But and area too saturated with organics will not provide a long-term base for good turfgrass. It will turn to muck. This is where the sand comes in, continually allowing materials to pass and the plant to breathe.