Sorry I didn't get to your question earlier.
How do archaeologists determine design vs. non-design?
By lots of research. We study the context in which tools are found in several ways: we observe extant "primitive" societies and their tool-making practices; we examine archaeological sites and the tools found in them; and we examine sites that are known to be natural and see what we find there. The latter might be river beds or rock slides or roads where traffic breaks up rocks. And many of us learn to make stone tools and artifacts as well. Replicative studies are usually very informative!
As part of his research, one of my professors in graduate school had a whole room filled with shelves, all of which were filled with "artifacts" found in streams and other natural deposits. He was able to study the differences between these and known tools and draw up some guidelines for differentiating between the two.
In the case of flaked stone, one of the most important traits to look for is bifacial flaking. That is very common in stone tools and very rare in nature.
Microscopic studies are also pretty useful, particularly use-wear studies. Regular use-wear is not found in nature, but is very common on certain types of stone tools.
And there are always some items that you can't easily tell one way or another. Then analyses of the material and where it originated, or studies of proteins in the pores of the stone, or other types of tests may provide additional clues.
In short, there are methods we can use to determine design from non-design. And we aren't afraid to talk about them.
Added: One fun kind of use-wear has been seen on sandstone and other soft stones. If a reasonably tough brush, such as manzanita, grows near the rock the wind can cause movement of the branches. This can result in the branches creating generally linear lines "drawn" or "carved" into the sandstone. The smoking gun is to find a branch still carving one of the lines.
Edited by Coyote, : addition
Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.