"Let's devise a way to purposefully burn the LED in such a way that current can go through." We have to keep in mind that not everything has to be by accident :) I have no idea how likely it is to be possible, though, you've got a point.

Why did you read that it's not the case? I read the opposite. That if the LED broke, you'd notice it because your camera would be on and the light would be off.

Not that the camera never turns on.

I would bet on the LED being parallel - otherwise sending more current through it will burn more power, generate more heat, and likely cause it to wear faster.

I think the point though is that it's not software controlled in any way: powering on the camera lights up the LED, and there's no way to bypass that with only software. Or at least that's the claim.