It is hard-wired, but it turns out there's a way to enable the camera while not lighting up that LED. The camera module has an input called 'standby' to which the LED is also connected. So normally if you put the cam in standby, the LED is off and if you take it out of standby then it's on. This is hardware and you can't use software to control that.
However the camera module, using an alternative firmware on the webcam's controller chip, can be told to disregard the state of that standby input and be controlled by a different input instead. Then, you can keep the standby input such that the LED stays off, while still using the camera module.