Could the near-threshold XYZ states be simply kinematic effects?

We demonstrate that the spectacular structures discovered recently in various experiments and named as X, Y and Z states cannot be purely kinematic effects. Their existence necessarily calls for nearby poles in the S matrix and they therefore qualify as states. We propose a way of distinguishing kinematic cusp effects from genuine S-matrix poles: the kinematic threshold cusp cannot produce a narrow peak in the invariant mass distribution in the elastic channel in contrast with a genuine S-matrix pole.