Lines around texture seems aren't usually caused by anti aliasing, since that's only doing multiple passes per fragment. If it isn't visible without anti aliasing, it won't be visible after either.
Texture problems are instead usually caused by mipmapping. It can make the seams a lot more imprecise.
It is by design. The solution is to clone a material manually and assign to sharedMaterial array. It doesn't affect other materials.
The next code will clone only second material, do you note you can't assign a new material directly, you must modify array:
Material materials = line.sharedMaterials;
materials = Instantiate(materials);