Some people refuse to till because it will disturb the soil fungi.
My theory is that fungi are not differentiated organisms (except when fruiting). They are multicellular, but they reproduce from fragments of hyphae. So I don't see why tilling would bother them even if individual fungal hyphae spread out over several feet (or mm? or yards?) in undisturbed soil. ten small small chunks of fungal hyphae ought to be able to do anything that one hunk ten times its size could do.
The individual fungus cells are tiny. They might be bothered if a Roto-Tiller operated like a food blender on "puree", but I think a Roto-Tiller only chops soil into peds larger than 1/4". A plow or fork turns up clods measured in inches.
But I'm no expert on soil mycology OR no-till theory. At home, I use a trenching shovel and fork when the clay elluviates into an impenetrable layer 12" down. Lately, my better beds haven't needed that.