I don't know that everyone goes to a private lesson with the same goals and expectations. Sometimes, I take privates with a rather general goal (like trying to lead more clearly and smoothly), while other times I'm trying to learn a specific step or sequence.I don't see how the two things are mutually exclusive. Of course the student is paying for help in improving, for which the teacher receives compensation. That doesn't mean the teacher isn't guiding (if teaching isn't guiding, I don't know what it is), and it doesn't mean that there aren't other benefits and motivations present, as well.
If my goal is more general, I'm much more receptive to the teacher going off on a tangent, but if the goal is more specific, then I want to stay on topic. Of course, my stress level (prior to the class) can be a factor as well, which is why I no longer will schedule a private after I get off from work.