Hi, In the file you've sent me, the group of faces visible in your sample image above were not in u,v = 0..1 range. But from the above image I see that they "were" in 0..1 range when you captured that, the file you sent me has not the same mapping as the one you showed here.
So I scaled them down to 0..1 range. but I got the same result when I did so. So I checked the rest of the faces and saw that there are many more faces in the negative UV space (zoom out in the unwrap editor). Moving them into 0..1 range also did not solve the problem.
I'll return to the solution promptly but before that I want to clearify something: if you intend to paint a texture, you should place all the UV vertices into 0..1 range (the area indicated by thick lines).
So why your model did not give a proper output even after putting all the UV vertices into 0..1 zone? Because it seems you've deleted some vertices in "Unwrap UVW" editor. These deleted vertices are actually assigned zero in u and v values. The below picture tags the faces taht use the deleted (therefore assumed to be u=v=0) texture vertices in red.
So the solution: re-do your mapping without deleting any texture vertices and beign sure that all the vertices are in 0..1 range in unwrap editor.