Does it matter whether the camera is on or off?
Don't get me wrong here, I'm not advocating for bodyworn cameras (or any cameras) in exam rooms, on or off-- I just find it interesting where the line is.
From my perspective, if you think your doctor is a creep enough to surreptitiously record you in the exam room using a camera that's on their face, then you can't rule out that they'd do it in ways that would be more difficult to detect. And if you do trust them not to record you with a hidden camera, then that trust should extend to a camera in plain sight.
At the end of the day, people have a right to be comfortable in these situations with their doctor, regardless of if it makes logical sense. I hope I didn't come off suggesting otherwise.