"I assume that's the full version of UV Mapper, not the free one?"

Yes, only UVMapper Pro can do that.

"The two faces should be touching each other at some points, but I don't see any artifacts."

To answer that, you'd probably need to be the developers of Firefly; and if you are, how come you haven't fixed it yet? :) You see my point, I think.

In general it seems all right for surfaces to be in close proximity to each other as long as it isn't extensive. We know they can intersect without harm, after all. Looking at the blocky nature of the coincident facet artefacts might lead one to believe that the facets had to be coincident over a certain minimum area before anything bad occurred; and further thought suggests that changing some render settings or other might cause this minimum to vary. This is pure hypothesis at the moment.

What I'd really like is proper WYSIWYG preview of single-sided mesh, and we aren't likely to get that here. Many's the time I've set up my perfect camera angle, only to find that there's a single-sided wall that I'd overlooked and my render shows only the backside of said wall. At least such a viewpoint renders quickly. :)