Just for the record, because it gets clear you know way better than me what you talking about, my assumptions to my point were 2:

1.- A single line belongs to an infinite number of planes
2.- A curve is the sum of tangent lines at a given reference point

Using these 2 assumptions, I can make a curve that will belong to an infinite number of planes, which will include the razor. I guess there is something wrong in those assumptions that would make my point not valid. And I guess this forum is not the place for this kind of discussion :P