You can indeed dig up clay that is "pottery ready." No sticks, or insects invovled unless you are careless. You just have to know where to go for the good stuff. It comes out of the ground nearly ready to use, though some conditioning is necessary.

My former brother-in-law has been a hobbiest potter since the early 70's. He went to a spot near the Kentucky River several times to "mine" his own clay. The biggest problem from his point of view was that it was much easier to buy it, especially after the novelty wore off.

Most modern potters aren't taught the same skills used by indignenous pot makers. Sort of like comparing using a compound bow in hunting to what was used in history.