Thanks! I just released it http://www.mariussilaghi.com/radial_symmetry.htm. It is a c++ plugin modifier and it works in 3ds max 9 and above(32/64 bit)
The automatic flatten UVs is the problem, you need to remove that modifier and in the render to texture settings change it to use existing UVs instead of automatic UVs.
Here's a way to create that only using spline and surface modifier in max : But i don't really think that max is the best software for that sort of stuff.
You can try the trial of the quad chamfer modifier I created. It has an Quad Intersection option that fixes the problem described by you automatically.