use of invariably

Invariably means "without variation or change, in every case."
However, I am not entirely sure why Dan Brown would use it in this sentence: "those who did not hear about the address via TV, invariably heard about it from neighbors."

I understand what he is trying to say. That is, they must have heard about it from neighbors. But to use the term invariably here, provided the definition given above, does not make a whole lotta sense to me

I would guess that he meant "inevitably". It's probably just an editing error.

I don't see the mystery. In every case that a person did not hear about the address via TV, the person in question heard about it from neighbors.

I think if I had to make the choice, it would depend on the context. "Invariably" would work if he were talking about a selection of people; maybe all the people that he had talked to. If he were just making a general description about people, then I think "inevitably" would sound better.

I think invariably works better in that sentence than inevitably -- it's the same as saying that in every instance, those who didn't hear it from the TV, heard it from their neighbors. Had there been occasional instance where they had heard it from a third source, I would then change "invariably" to "generally" or "mostly", but if the neighbors were truly the only alternate source to the television, "invariably" works fine.