How do topological insulators violate Nielsen-Ninomiya Theorem?

Question

I am under the impression that topological insulators have a distinguishing characteristic where they have an odd number of Dirac points that intersect band gaps at the Fermi energy.
However, this seems to violate the Nielsen-Ninomiya theorem which states there is an even number of states of opposite chirality. I take this to mean there should be an even number of Dirac fermions.
a topological insulator could violate this theorem if it did not have translation symmetry, but I understand that they do. How do they manage to obtain an odd number of Dirac points then?
Edit:
To respond to the comment below,
First, I'm using the term point and  fermion (referring to the emergent quasiparticle that crosses that point) interchangeably, is that accurate?
Secondly, the comment seems to imply that odd numbers of Dirac fermions do not violate the NN theorem because it has a net chirality of zero. My confusion lingers because topological insulators do have net transport in their edge states which after further reading, seems to be a result of your namesake, a chiral anomaly.
The Adler-Bell- Jackiw anomaly
  is mentioned in section of 1.3 and 2.6 of Witten's notes here. Are topological insulators a realization of this anomaly?

Leviathan · Accepted Answer

They don't.
Sometimes people make effective models to describe for example only one edge of a 2 dimensional topological insulator. Then you get to describe a band with only 1 chirality. That would violate the NN theorem.
But with the full TI taken into account, the NN theorem is preserved.
When you see a band structure with only one surface state crossing the Fermi energy, this is strictly speaking wrong. This is always under the assumption that you look at only one edge.

How do topological insulators violate Nielsen-Ninomiya Theorem?

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