I have looked at my kids’ pediatrician visit summaries, and they will state “doctor did this and that”, when I know for a fact the doctor did not. So I have to send a mychart message to document that the doctor did not do those things.
Now, I understand that excessive liability is probably driving doctors to do unnecessary things and so 95% of the time, there is no ill intent, but rather shrewd judgment of not wasting time, however writing (or copy pasting) a false visit summary is not the answer.
Note: All of this is U.S. perspective, I have no idea about healthcare anywhere else.
Given how hard it is to even find half-decent doctors even taking new patients, or having appointments available this quarter let alone soon, the doctor likely doesn't need you nearly as much as you probably need a doctor. They're going to be fully booked even if they ask you to leave and decline to be filmed, so they don't have any reason to consent to it. This is one place where the "try to make the customer happy" conventional wisdom about transactional relationships seems to not apply one iota.