  Non-existence of a local hidden variables (LHV) model for a phenomenon
benchmarks its use in device-independent quantum protocols. Nowadays
photon-number resolving weak-field homodyne measurements allow realization of
emblematic gedanken experiments. Alas, claims that we can have no LHV models
for such experiments on (a) excitation of a pair of spatial modes by a single
photon, and (b) two spatial modes in a weakly squeezed vacuum state, involving
constant local oscillator strengths, are unfounded. For (a) an exact LHV model
resolves the dispute on the "non-locality of a single photon" in its original
formulation. It is measurements with local oscillators on or off that do not
have LHV models.
