Picture looks fine to me also. When inspecting a revolver for purchase I hold it up to light and look at that exact spot. If I see a just a sliver of light I am happy. To much bothers me way more.

The edge of a piece of paper may be harder to start than a steel feeler gauge, plus the calipers may well be compressing the paper a bit.
.004 is about as tight as I would like. But, lets say you had a revolver that measured .002 with cylinder pressed forward by hand, it would fire and function fine for a number of rounds and then any built up on cylinder and or barrel face would cause the cylinder to start dragging. With a real tight gap this could occur rapidly, depending on powder, bullet type, tolerance of cylinder to barrel alignment.

Great thing is a tight gap is easily fixed. Not so with a tight gap.