  We recall the importance of recognizing the different mathematical nature of
various concepts relating to PT-symmetric quantum theories. After clarifying
the relation between supersymmetry and pseudo-supersymmetry, we prove
generically that nonlinear pseudo-supersymmetry, recently proposed by Sinha and
Roy, is just a special case of N-fold supersymmetry. In particular, we show
that all the models constructed by these authors have type A 2-fold
supersymmetry. Furthermore, we prove that an arbitrary one-body quantum
Hamiltonian which admits two (local) solutions in closed form belongs to type A
2-fold supersymmetry, irrespective of whether or not it is Hermitian,
PT-symmetric, pseudo-Hermitian, and so on.
