  The dwarf galaxy NGC 3109 is receding 105 km/s faster than expected in a
$\Lambda$CDM timing argument analysis of the Local Group and external galaxy
groups within 8 Mpc (Banik \& Zhao 2018). If this few-body model accurately
represents long-range interactions in $\Lambda$CDM, this high velocity suggests
that NGC 3109 is a backsplash galaxy that was once within the virial radius of
the Milky Way and was slingshot out of it. Here, we use the Illustris TNG300
cosmological hydrodynamical simulation and its merger tree to identify
backsplash galaxies. We find that backsplashers as massive ($\geq 4.0 \times
10^{10} M_\odot$) and distant ($\geq 1.2$ Mpc) as NGC 3109 are extremely rare,
with none having also gained energy during the interaction with their previous
host. This is likely due to dynamical friction. Since we identified 13225 host
galaxies similar to the Milky Way or M31, we conclude that postulating NGC 3109
is a backsplash galaxy causes $>3.96\sigma$ tension with the expected
distribution of backsplashers in $\Lambda$CDM. We show that the dark matter
only version of TNG300 yields much the same result, demonstrating its
robustness to how the baryonic physics is modelled. If instead NGC 3109 is not
a backsplasher, consistency with $\Lambda$CDM would require the 3D timing
argument analysis to be off by 105 km/s for this rather isolated dwarf, which
we argue is unlikely. We discuss a possible alternative scenario for NGC 3109
and the Local Group satellite planes in the context of MOND, where the Milky
Way and M31 had a past close flyby $7-10$ Gyr ago.
