That's not a corner case, that's just more advanced math. No one ever claimed that triangulation on a plane is the same as triangulation on the surface of a sphere.
Like the other response you basically said context is everything. You just prefer to call the context axioms. What is context free here is the arithmetic.
Arithmetic still depends on which ring/field axioms you're using. :) I think you would have to agree, though, that axioms are a much more tractable kind of context than "a whole honking physical situation with atoms and entropy", which I think is the real kernel of the article.