  The recently observed superconductivity in twisted bilayer graphene emerges
from insulating states believed to arise from electronic correlations. While
there have been many proposals to explain the insulating behaviour, the
commensurability at which these states appear suggests that they are Mott
insulators. Here we focus on the insulating states with $\pm 2$ electrons or
holes with respect to the charge neutrality point. We show that the theoretical
expectations for the Mott insulating states are not compatible with the
experimentally observed dependence on temperature and magnetic field if, as
frequently assumed, only the correlations between electrons on the same site
are included. We argue that the inclusion of non-local (inter-site)
correlations in the treatment of the Hubbard model can bring the predictions
for the magnetic and temperature dependencies of the Mott transition to an
agreement with experiments and have consequences for the critical interactions,
the size of the gap, and possible pseudogap physics. The importance of the
inter-site correlations to explain the experimental observations indicates that
the observed insulating gap is not the one between the Hubbard bands and that
antiferromagnetic-like correlations play a key role in the Mott transition.
