  In current studies for testing Bell inequalities at colliders, the
reconstruction of spin correlations from scattering cross-sections relies on
the bilinear form of the spin correlations, but not all local hidden variable
models (LHVMs) have such a property. To demonstrate that a general LHVM cannot
be rule out via scattering cross-section data, we propose a specific LHVM,
which can exactly duplicate the same scattering cross-section for particle
production and decay as the standard quantum theory, making it
indistinguishable at colliders in principle. Despite of this, we find that
reconstructing spin correlations through scattering cross-sections can still
exclude a broad class of LHVMs, e.g., those models employing classical spin
correlations as a surrogate for quantum spin correlations.
