  The kagome metals AV$_3$Sb$_5$ (A=K,Rb,Cs) present an ideal sandbox to study
the interrelation between multiple coexisting correlated phases such as charge
order and superconductivity. So far, no consensus on the microscopic nature of
these states has been reached as the proposals struggle to explain all their
exotic physical properties. Among these, field-switchable electric
magneto-chiral anisotropy (eMChA) in CsV$_3$Sb$_5$ provides intriguing evidence
for a rewindable electronic chirality, yet the other family members have not
been likewise investigated. Here, we present a comparative study of
magneto-chiral transport between CsV$_3$Sb$_5$ and KV$_3$Sb$_5$. Despite their
similar electronic structure, KV$_3$Sb$_5$ displays negligible eMChA, if any,
and with no field switchability. This is in stark contrast to the
non-saturating eMChA in CsV$_3$Sb$_5$ even in high fields up to 35 T. In light
of their similar band structures, the stark difference in eMChA suggests its
origin in the correlated states. Clearly, the V kagome nets alone are not
sufficient to describe the physics and the interactions with their environment
are crucial in determining the nature of their low-temperature state.
