  Ultra-faint dwarf galaxies (UFDs) are commonly found in close proximity to
the Milky Way and other massive spiral galaxies. As such, their projected
stellar ellipticity and extended light distributions are often thought to owe
to tidal forces. In this paper, we study the projected stellar ellipticities
and faint stellar outskirts of tidally isolated ultra-faints drawn from the
'Engineering Dwarfs at Galaxy Formation's Edge' (EDGE) cosmological simulation
suite. Despite their tidal isolation, our simulated dwarfs exhibit a wide range
of projected ellipticities ($0.03 < \varepsilon < 0.85$), with many possessing
anisotropic extended stellar haloes that mimic tidal tails, but owe instead to
late-time accretion of lower mass companions. Furthermore, we find a strong
causal relationship between ellipticity and formation time of an UFD, which is
robust to a wide variation in the feedback model. We show that the distribution
of projected ellipticities in our suite of simulated EDGE dwarfs matches well
with that of 21 Local Group dwarf galaxies. Given the ellipticity in EDGE
arises from an ex-situ accretion origin, the agreement in shape indicates the
ellipticities of some observed dwarfs may also originate from a similar
non-tidal scenario. The orbital parameters of these observed dwarfs further
support that they are not currently tidally disrupting. If the baryonic content
in these galaxies is still tidally intact, then the same may be true for their
dark matter content, making these galaxies in our Local Group pristine
laboratories for testing dark matter and galaxy formation models.
