  In general relativity (GR), the internal dynamics of a self-gravitating
system under free-fall in an external gravitational field should not depend on
the external field strength. Recent work has claimed a statistical detection of
an `external field effect' (EFE) using galaxy rotation curve data. We show that
large uncertainties in rotation curve analyses and inaccuracies in published
simulation-based external field estimates compromise the significance of the
claimed EFE detection. We further show analytically that a qualitatively
similar statistical signal is, in fact, expected in a $\Lambda$-cold dark
matter ($\Lambda$CDM) universe without any violation of the strong equivalence
principle. Rather, such a signal arises simply because of the inherent
correlations between galaxy clustering strength and intrinsic galaxy
properties. We explicitly demonstrate the effect in a baryonified mock catalog
of a $\Lambda$CDM universe. Although the detection of an EFE-like signal is
not, by itself, evidence for physics beyond GR, our work shows that the
$\textit{sign}$ of the EFE-like correlation between the external field strength
and the shape of the radial acceleration relation can be used to probe new
physics: e.g., in MOND, the predicted sign is opposite to that in our
$\Lambda$CDM mocks.
