membrane locking and CST trangle

I often read on books that linear triangles do not have membrane locking for large deformations of plates/shells. I completely don't understand how this is possible. If one uses the well-known CST, stretching is measured as the increase in lenght of each edge of the triangle. Then, in the limit of the membrane stiffness going to infinity, clearly the solution cannot approximate any bending-dominated state, but rather it will be always rigid on general meshes (i.e. Minkowski theorem for convex bodies), allowing at most bending about few lines on very regular ones. What am I missing?