We use a symmetry-motivated approach to analysing X-ray pair distribution functions to study the mechanism of negative thermal expansion in two ReO3-like compounds; ScF3 and CaZrF6. Both average and local structure suggest that it is the flexibility of M-F-M linkages (M = Ca, Zr, Sc) due to dynamic rigid and semi-rigid "scissoring" modes that facilitates the observed NTE behaviour. The amplitudes of these dynamic distortions are greater for CaZrF6 than for ScF3, which corresponds well with the larger magnitude of the thermal expansion reported in the literature for the former. We show that this flexbility is enhanced in CaZrF6 due to the rock-salt ordering mixing the characters of two of these scissoring modes. Additionally, we show that in ScF3 anharmonic coupling between the modes responsible for the structural flexibility and the rigid unit modes contributes to the unusually high NTE behaviour in this material.