I don't think they would waste a high value capacitor just to keep a led lit for longer, also a led directly lit by a capacitor would be noticeable by slowly dimming when the capacitor discharges. It's more likely that the signal driving the led comes out of a monostable implemented in code: pin_on() drives the led on; pin_off() waits n secs then drives the led off.

This is Apple, so that assertion isn’t guaranteed valid like it would be for non-enterprise HP or Lenovo. They absolutely would invest in a capacitor if that’s what it takes, as they are maximally focused on camera privacy concerns and have made a point of that in their security marketing over time; or else they wouldn’t be allowing hardware security engineers to brag about it, much less talk publicly about it, at all.

EDIT: It’s not just a capacitor, it’s a full custom chip, that can’t be software-modified, that keeps the light on for 3 seconds. https://news.ycombinator.com/item?id=42260379

Logic on an already existing ASIC is going to be cheaper than a capacitor.

This is counter-intuitive enough to warrant further explanation.

If you are designing an ASIC for the camera, you can include all the required logic gates to control the LED for a cost that is close to zero. It wouldn't impact the production cost of the ASIC, whereas a capacitor is an additional item in the BOM (and to be charged it requires current, more than the LED, so the driver in the IC must be bigger).