  The realistic interpretation of classical theory assumes that every classical
system has well-defined properties, which may be unknown to the observer but
are nevertheless part of reality and can in principle be revealed by
measurements. Here we show that this interpretation can in principle be
falsified if classical systems coexist with other types of physical systems. To
make this point, we construct a toy theory that (i) includes classical theory
as a subtheory and (ii) allows classical systems to be entangled with another
type of systems, called anti-classical. We show that our toy theory allows for
the violation of Bell inequalities in two-party scenarios where one of the
settings corresponds to a local measurement performed on a classical system
alone. Building on this fact, we show that measurements outcomes in classical
theory cannot, in general, be regarded as pre-determined by the state of an
underlying reality.
