Another rule of thumb I like to apply when mix-and-matching different levels of tests: how visible would a bug be in higher level tests? If things will fail in obvious ways, a unit test will give no benefit besides narrowing down the bug location in case of a failure.

But if symptoms would likely be too subtle to stand out, e.g. a typical bug would manifest itself in results that seem plausible despite being wrong, then it's a strong indication for unit tests.