  Stacking two graphene layers twisted by the 'magic angle' $\theta \approx
1.1^\circ$ generates flat energy bands, which in turn catalyzes various
strongly correlated phenomena depending on filling and sample details. At
charge neutrality, transport measurements reveal superficially mundane
semimetallicity (as expected when correlations are weak) in some samples yet
robust insulation in others. We propose that the interplay between interactions
and disorder admits either behavior, even when the system is strongly
correlated and locally gapped. Specifically, we argue that strong interactions
supplemented by weak, smooth disorder stabilize a network of gapped quantum
valley Hall domains with spatially varying Chern numbers determined by the
disorder landscape--even when an entirely different order is favored in the
clean limit. Within this scenario, sufficiently small samples that realize a
single domain display insulating transport characteristics. Conversely,
multi-domain samples exhibit re-emergent massless Dirac fermions formed by
gapless domain-wall modes, yielding semimetallic behavior except on the
ultra-long scales at which localization becomes visible. We discuss
experimental tests of this proposal via local probes and transport. Our results
highlight the crucial role that randomness can play in ground-state selection
of twisted heterostructures, an observation that we expect to have further
ramifications at other fillings.
