The first link you posted says that 29% of the land is used for pasture and 15% is used for crops (which will include both human and animal).

So yes, most cows are eating grass like a wandering herd.

The data doesn't prove either point. For all we know, a very low number of cattle are being grazed on those 29%. Or a lot of them. We don't know.

That doesn't follow. The chart is counting the number of acres of land which are used for specific purposes, not the number of cattle being raised on that land. And the category you're counting as "pasture" encompasses rangeland as well, which is used at an extremely low density (often as low as 1 head of cattle per 10 acres).