ok, I took a look at the scene and the problem is caused by the object's geometry. It is actually concave, leading to self-shadowing (made visible due to big color spread value). It is tricky to see, since the non-convex objects are the individual quads.
This is one of the problematic polygons. I created a lines connecting its opposing pairs of vertices:
This is the same polygon from angle - you can see it is concave:
This is the render with default non-convex tesselation:
And here I manually change the tesselation of the quad to produce convex result:
