You are correct in all the points you make in your question:
1) Anesthesia encompasses many shades of gray; the deeper the sleep, the less you breath, until, ultimately, a breathing tube and ventilator are required. While most physicians would agree that once a patient is on a ventilator it is "general anesthesia", some would argue even patients breathing for themselves in deep sleep may qualify as "general anesthesia" -- just without a breathing tube. There are some IV medications that in moderate doses produce sedation, and in higher doses produce general anesthesia. Propofol is one such drug.
2) Rhinoplasty can be accomplished safely either way - either under general, or under sedation. While a breathing tube does lower the risk of having blood or secretions enter the airway, the depth of anesthesia required to "tolerate the tube" in your windpipe is much deeper than necessary for painless rhinoplasty. It also comes with increased recovery, and the increased risk of the deeper anesthesia itself. Interestingly, bleeding is more frequent and more copious under general anesthesia than under sedation, due to relaxation of the blood vessel walls by the general anesthetic.
3) Recovery is easier under sedation than under general. Fewer drugs + less invasive procedure (no tube) = easier recovery.
As a rule, I prefer twilight for my septorhinoplasty cases. It is certainly more work for the anesthesia provider and surgeon than general anesthesia, but I feel that the risk and recovery profile is better.
Best of luck!