Since such triangles are not defining a surface, they should - mathematically - not have any facing. So, i would assume that the outcome of face-culling is implementation defined. On your hardware (which is it?) it seems to not to cull such faces at all.
Degenerate is probably a better term for the duplicate vertex case, though 3 collinear points would also produce a zero area triangle, without any duplicates. In other words, a triangle can “degenerate” into a line or a point.