To get back to the opening post, I would question whether the fragments found were actually pottery. It depends on how you define the term.

If you look at the photo in the article, you'll see that the fired shards bear the impression of straw-like material.

The general consensus among archaeologists is that basket making predates pottery, and that some cultures lined their baskets with wet clay to make them less porous. When worn out baskets were tossed into fires, the clay linings were heated, leaving fired shards behind. But are those shards really pottery?

I don't think so. They're clay basket liners which were fired by accident, not intentionally. The use of unfired clay as a basket sealant was an intermediate step in the evolution of pottery, but not actual pottery-making. That innovation occurred when someone decided to forego the basket and make a vessel directly from moist clay and then intentionally place it in a fire pit.