We find the single exciton's fine structure splitting (FSS), which splits its
degenerate ground state manifold into singlets, nearly vanishes in highly
asymmetric quantum dots due to the cancellation of splitting effects with
markedly different origin. The dots simulated are those that emerge on top of
etch pits through the droplet epitaxy growth process; these etch pit dots break
square (C4v) spatial symmetry, which has been previously associated with
small FSS. Configuration interaction calculations predict a vanishing FSS at a
specific finite etch pit displacement from the center of the dot, for a
structure far from square symmetry. We thus predict that highly asymmetric
quantum dots may still display negligible fine structure splitting, providing
new avenues for high-fidelity generation of indistinguishable, polarization
entangled photon pairs on demand