There's a lot of places where we'd have catastrophic consequences if we had wrong beliefs about pure mathematics. For example, public-key crypto would fall apart if mathematicians were severely mistaken about finite groups and their relationship to prime numbers. And we couldn't be very wrong about real analysis before we'd notice something the matter with calculus.

I would have said that math is a degenerate case for such a heuristic because we so seldom are wrong about it.