I mean, even if you could turn on the mic/camera, I would think you still need to possibly save it to storage for retrieval later which pretty much requires the OS to be running.
Otherwise, maybe, you could somehow transmit the data but that would require the ability to communicate with the device via Bluetooth/WiFi and for the data from the camera to be passed to the wireless interface.
Unless a device was designed with that sort of functionality, I'm not sure how the NSA could just turn that on.
Jumping from one exploit target to another in a chain is pretty much how all modern exploits work. To say that because they would need to find an exploit in the USB driver (or some other hardware or software interface), not only states the obvious, but more importantly misses the point: it's far more plausible than most engineers intuitively believe.
The depth of modern exploit chains is incredible, and while the conceptual difficulty has gone up the pace hasn't seemed to abate, which is clear evidence that our intuition about "too difficult" and about the elasticity of the exploit supply and demand curves is woefully inadequate to accurately gauge risk.
Part of the problem is that the complexity of the systems grows at the same time as improvements in security and correctness. Sometimes it grows faster, sometimes slower, but it's dynamic.
I believe that this has actually been pretty well established in the community, but I don’t have the evidential links immediately at hand.
The tone of incredulity in your comment suggests, as if this practice is extraordinary, when it would be considered SOP ─ tools and crims behind bars make the most unlikely bedfellows.
Also, one of the Snowden disclosures was that apparently the NSA can power on the cameras and mics of Android phones even when the phone is off. I don't know exactly how it works, but it does, probably based off the residual current drawn from the battery and the circuitry that handles the power button. Smartphones are basically never safe, although I've heard iPhones are significantly safer than Android.