  Pristine bilayer graphene behaves in some instances as an insulator with a
transport gap of a few meV. This behaviour has been interpreted as the result
of an intrinsic electronic instability induced by many-body correlations.
Intriguingly, however, some samples of similar mobility exhibit good metallic
properties, with a minimal conductivity of the order of $2e^2/h$. Here we
propose an explanation for this dichotomy, which is unrelated to electron
interactions and based instead on the reversible formation of boundaries
between stacking domains (`solitons'). We argue, using a numerical analysis,
that the hallmark features of the previously inferred many-body insulating
state can be explained by scattering on boundaries between domains with
different stacking order (AB and BA). We furthermore present experimental
evidence, reinforcing our interpretation, of reversible switching between a
metallic and an insulating regime in suspended bilayers when subjected to
thermal cycling or high current annealing.
