They do indeed, although not everybody does. It is a personal preference and something to be thought about. There is no obligation, and there is no expectation. The idea is that by reclining comfortably and not having eye contact (or a video link when working online) you are less distracted by the presence of another person and more at ease to let your thoughts drift and your mind wander and to get in touch with your internal world. Many patients find this freeing and helpful. Some prefer to keep eye contact. Either way, good and meaningful work can happen.