you can dig in the soil in a no-till, most do. fukoka advocates "doing nothing" but in reality, processes still need to occur, he is just really on nature and positioning to achieve that. For instance if a pig rooting around disturbs and "tills" the soil, similar to if you just went out and carefully rooted around for potatoes yourself. Essentially you are doing "nothing", the tillage is just a great after effect of looking for food.
Even tilling the soil occassionally can occur in no till practices [it happens], but soil types are all over the board, so what works for one soil may be totally irrelevant in another, something to keep in mind.