This depends on how the light is implemented -- if it's implemented in the camera module itself it's pretty bulletproof, but i would bet it's just a gpio to the processor on most of these devices and controlled by the os anyway. I could be wrong about that, but I err on the side of caution. I keep my phone in a bag most of the time.

Treat every gun as if it's loaded, and every camera as if it's filming.

Yes but also this has never been an issue on any phones (i.e. never heard a complaint), and you take that to the toilet. By comparison a laptop camera has much less access to your private life.

People who are truly worried about cameras will cover it regardless of indicator.