  When should a given operational phenomenology be deemed to admit of a
classical explanation? When it can be realized in a generalized-noncontextual
ontological model. The case for answering the question in this fashion has been
made in many previous works, and motivates research on the notion of
generalized noncontextuality. Many criticisms and concerns have been raised,
however, regarding the definition of this notion and of the possibility of
testing it experimentally. In this work, we respond to some of the most common
of these objections. One such objection is that the existence of a classical
record of which laboratory procedure was actually performed in each run of an
experiment implies that the operational equivalence relations that are a
necessary ingredient of any proof of the failure of noncontextuality do not
hold, and consequently that conclusions of nonclassicality based on these
equivalences are mistaken. We explain why this concern in unfounded. Our
response affords the opportunity for us to clarify certain facts about
generalized noncontextuality, such as the possibility of having proofs of its
failure based on a consideration of the subsystem structure of composite
systems. Similarly, through our responses to each of the other objections, we
elucidate some under-appreciated facts about the notion of generalized
noncontextuality and experimental tests thereof.
