There would be nothing left for them to pick at if they were 100% grass fed. The microbes in the cow's rumen will have broken down the plant fiber and whatever is left will be indigestible.
I've heard that there are lots of undigested seeds and other partially digested matter in cow manure. Have I just heard wrong ? Can pigs still get fiber and vitamins from it? If fresh cow manure is tossed into a pig pen, would tje pigs at least root through and spread it around?