My instructors always asked me how long to push IV meds for, I wasn't allowed to give anything until I did that. As far as actually doing it, I guess it's a personal decision that the instructor bases on knowledge of the student and the trust that they decide to place in them. If we had students that were unsure about a certain med, or were giving something like 80mg Lasix IV, the instructor would go with, or ask that another (clinically strong) student went with them, unless the RN preferred to do it. In some of my rotations, we weren't allowed to give narcotics at all. Of course if it's a high risk medication, I can understand the nurse (or CI) wanting to observe. If we ever had vasoactive meds or a large dose of Lasix or pain meds and the pt's vitals were iffy (but no parameters), our instructor would tell us she wasn't comfortable with us giving the med just in case something happened, but it would be up to the RN if he/she wanted to give it.
I think it has to be a case by case decision. I would be kind of insulted if my instructor went with me my last semester to make sure that I passed morning meds correctly on every patient. Like I said, high-risk medications or those with the potential for harm (like your morphine example) I can understand. But there also needs to come a point where the instructor isn't telling you when to give/hold medications and is instead tests your clinical judgment to see that you can make sound decisions come graduation day, but still has the opportunity to intervene if you make the wrong decision. That, for us, occurred in the medication room in most instances.