Why are cube map S-T-R axes left-handed?

I wonder why the cube map S-T-R axes are left-handed(where the R axis points into the screen) instead of being right-handed(where the R axis points out of the screen) when everything else in OpenGL is right-handed?
Does this mean I’d have to invert the r-coord(by doing a -1 scale along the z-axis via the tex matrix or even the texgen planes?) of the normal vector generated at every vert by texgen in GL_NORMAL_MAP_EXT mode? (since the vector would’ve been defined in eye space which is right-handed)