  We use a symmetry-motivated approach to analyse neutron pair distribution
function data to investigate the mechanism of negative thermal expansion (NTE)
in ReO$_3$. This analysis shows that the local structure of ReO$_3$ is
dominated by an in-phase octahedral tilting mode and that the octahedral units
are far less flexible to scissoring type deformations than the octahedra in the
related compound ScF$_3$. These results support the idea that structural
flexibility is an important factor in NTE materials, allowing the phonon modes
that drive a volume contraction of the lattice to occupy a greater volume in
reciprocal space. The lack of flexibility in ReO$_3$ restricts the NTE-driving
phonons to a smaller region of reciprocal space, limiting the magnitude and
temperature range of NTE. In addition, we investigate the thermal expansion
properties of the material at high temperature and do not find the reported
second NTE region. Finally, we show that the local fluctuations, even at
elevated temperatures, respect the symmetry and order parameter direction of
the observed $P4/mbm$ high pressure phase of ReO$_3$. The result indicates that
the motions associated with rigid unit modes are highly anisotropic in these
systems.
