Michael,
Thanks for the detailed explanation! I did not know that about the 0.005 threshold tolerance. That could be used for some good later.

Sorry about that, here is a simplified file: http://k4icy.50webs.com/tutorials/surface_join_area_ex01.3dm
The Orange and Green surfaces are the ones in question.

And honestly now, I can't say that I remember exactly what method or workflow I used to create that set of surfaces.
I may have started with an extrusion of the gap-seam shape that was run the length of the box from end to end. Then I may have performed a Boolean Intersect of the extrusion using a closed curve set created from the inside lip of the box.
Hmmm, and I can think of another way or two that set may have been created.

It's great to know that there are so many ways to skin the proverbial cat.

But with the provided file, you can zoom in close and see that the two surface don't exactly meet.