What is wrong with making a unit test a friend of the class it is testing?

You should consider that there are different styles and methods to test: Black box testing only tests the public interface (treating the class as a black box). If you have an abstract base class you can even use the same tests against all your implementations.

If you use White box testing, you might even look at the details of the implementation. Not only about which private methods a class has, but what kind of conditional statements are included (i.e. if you want to increase your condition coverage because you know that the conditions were hard to code). In white box testing, you definitely have "high coupling" between classes/implementation and the tests which is necessary because you want to test the implementation and not the interface.

As bcat pointed out, it's often helpful to use composition and more but smaller classes instead of many private methods. This simplifies white box testing because you can more easily specify the test cases to get a good test coverage.

Ideally, you shouldn't need to unit test private methods at all. All a consumer of your class should care about is the public interface, so that's what you should test. If a private method has a bug, it should be caught by a unit test that invokes some public method on the class which eventually ends up calling the buggy private method. If a bug manages to slip by, this indicates that your test cases don't fully reflect the contract you wish your class to implement. The solution to this problem is almost certainly to test public methods with more scrutiny, not to have your test cases dig into the class's implementation details.

Again, this is the ideal case. In the real world, things may not always be so clear, and having a unit testing class be a friend of the class it tests might be acceptable, or even desirable. Still, it's probably not something you want to do all the time. If it seems to come up often enough, that might a sign that your classes are too large and/or performing too many tasks. If so, further subdividing them by refactoring complex sets of private methods into separate classes should help remove the need for unit tests to know about implementation details.