I don't get the worry about the NP complete problem of tiling a finite area.

Yes, of course, if you allow arbitrary adjacency rules then tiling is going to be NP complete but the goal here is to generate realistic tilings then it's reasonable to assume that if you have a compact connected region that obeys the tiling rules and any square there is some tile that is allowed to be placed in that square.

I mean this is how the real world works. You don't have holes in reality so if it's possible to have a part of the world that looks like such-and-such there must be a valid description of the stuff next to it.