This is where possession and permission to operate the vehicle matters. The dealership has both of these elements when you drop it off for service.
So let's finish this story to make it an apples-to-apples comparison, or at least a little closer to that.
You would need to drop the vehicle off in my driveway, hand me over the keys, and provide me with permission to operate the vehicle. In this scenario, I could absolutely turn off your dashcam if I chose to while the vehicle was under my control.
They can also adjust your seats, turn off the radio (maybe change the station, etc.)
I understand you don't like the idea of the camera being turned off, but that doesn't mean they can't do it.