From my understanding organic matter can consist of plant and or animal waste at various stages of decomposition, cells and tissues of soil microbes, and substances that soil microbes synthesize with. So when i smash the cover crop, some dies off and creates a brown mulch. I know my microbes are active and is balancing my beds. Mycelium is adding in composting brown matter and the red wiggers has been munching on the fresh greens.
Yes I do agree. But manure or other animal based amendments can raise Potassium levels to the degree that is undesirable in a no-till perpetual grow situation. It's like why I try and keep P levels low if possible in my mulches. Timothy hay or whatever straw seem to keep that in-line to avoid those possible excesses. That's thee other reason I think hay/stray is okay.