  Violations of Bell inequalities have been an incontestable indicator of
non-classicality since the seminal paper by John Bell. However, recent claims
of Bell inequalities violations with classical light have cast some doubts on
their significance as hallmarks of non-classicality. Here, we challenge those
claims. The crux of the problem is that such classical experiments simulate
quantum probabilities with intensities of classical fields. However, fields
intensities measurements are radically different from single-photon detections,
which are primitives of any genuine Bell experiment. We show that this
fundamental difference between field intensities measurements and single photon
detections shifts the classical bound of relevant Bell inequalities to its
algebraic limit, leaving no place for their violations.
