How is it accidental? The code can only do what its public interfaces expose. This indirectly (not accidentally) exercises the private methods.
If all the public interface test cases pass, isn't that enough?
If all the public interface test cases pass, isn't that enough?
Sometimes there are well-defined processes for performing a task, and that task is performed in only one place in the system. Therefore the details of the process can be kept class private inside of the only consumer. That doesn't mean that the processes should never be tested. If the task is cumbersome to set up or runs slowly then there is good reason to test the internal parts of the process which can be tested with dozens, hundreds or even thousands of permutations of input data cheaply and efficiently. Always relying on the large-scale tests to hit every combination of inputs for a well understood subroutine can be inefficient.
You could make the argument that this well-understood process could be broken out into its own class/package/module and tested with its own public interface, but if there really is only one consumer then that's kind of a strange trade-off to make in many cases.
That's how I develop in general: a "component" does not exist because it has multiple-clients, but because it is a conceptual piece of logic that makes sense to document and test in isolation. It allows to define what is the public API of this component and what isn't. This is how software scales and stays maintainable over time IMO.
But even deeper, it is "accidental" because you are not testing contracts on the public APIs, you're testing the private functions through a layer higher. When the implementation changes, you have coupled your tests so tightly to the implementation that they are useless for regression testing. If not, then you actually aren't testing the private function at all, you're just hitting some parts by coincidence.
When I see tests that are orders of magnitude larger than the units they’re testing and contain mocked references that are used 7 stack frames deep I know the author had a fundamental misunderstanding of how to write helpful and maintainable tests.