Nice to see you're making progress.
No, he does not use texturing, so it's not a sampling artifact. I suspect something with the depth test (z-fighting): Lines and Quads are approximately at the same depth, but only approximately. Play around with the DepthBias render state .
They are realy at the same depth. I'm drawing it from 1 vertexBuffer, just with different indexes. Their position is the same. I'm drawing tringles at first, then lines over them.
d3dDevice.SetStreamSource(0, vertices, 0, Marshal.SizeOf(typeof(Vertex)));
d3dDevice.VertexFormat = VertexFormat.Position | VertexFormat.Diffuse;
d3dDevice.Indices = triangles;
d3dDevice.DrawIndexedPrimitive(PrimitiveType.TriangleList, 0, 0, totalPointsCount, 0, totalPointsCount / 2);
d3dDevice.VertexFormat = VertexFormat.Position;
d3dDevice.Indices = lines;
d3dDevice.DrawIndexedPrimitive(PrimitiveType.LineList, 0, 0, totalPointsCount, 0, totalPointsCount);
Playing with DepthBias render state do not give any results...