In the situation I am thinking of, the tests that select successful modifications are, almost by definition, integration tests, because with a big ball of mud, you don't know what the proper specification for the components are, and they don't have clear interfaces.

By 'tests' I am including live failures, which are also a feature of mudballs.

A distributed system is always much more difficult to test than a functionally-equivalent localized version. That's not, of course, a reason to give up on testing, but one must be realistic about how much faith one can put in it to make up for an inadequate use of abstraction and separation of concerns.