I found that with GISD checked (all default settings, so basic filter, no DOF), the dreaded lines were back (third part). No GISD, no lines (second part). But the strange thing is that the lines were already there before GISD was computed (see the part of this screendump with the black patches still to be rendered; first part).
Basic object test with an alpha opacity layer, no translucency, this time unpremultiply unchecked.
And a question that popped up before this happened; what vertices can TG handle best, triangles or squares? These hides were put through Poseray, so are triangles.