I found out something interesting. I exported Collada versions of the test file that gives the artifacts, and an export of the same model after redrawing two faces. When I imported them back into SketchUp, the artifact export still showed artifacts in LayOut, and the redrawn face export still looked good in LayOut.
I checked the Collada files for what is different, and found that the bad one has two polygons in it (instead of only being polylists). If I copied those into the good export, then imported back into SketchUp, two extra lines showed up, one of which was invisible.
It seems as if a couple of polygons were created in the same place as a polylist was already describing, at least in Collada terms.
Whether solid tools made those, or why they exist, I don’t know.