  We show that the respective oversights in the von Neumann's general theorem
against all hidden variable theories and Bell's theorem against their
local-realistic counterparts are homologous. Both theorems unjustifiably assume
the additivity of expectation values within hidden variable theories to derive
their respective conclusions. However, for non-commuting observables, the
equivalence of a sum of expectation values and the expectation value of the sum
of measurement results, although respected within quantum mechanics, need not
hold for hidden variable theories, regardless of specific characteristics such
as local realism they may respect. Once this oversight is ameliorated from
Bell's argument and local realism is implemented correctly, the bounds on the
CHSH correlator work out to be ${\pm2\sqrt{2}}$ instead of ${\pm2}$, thereby
mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by
the Bell-test experiments is not local realism but the additivity of
expectation values.
