Perhaps interestingly, many/most digital cameras are sensitive to IR and can record, for example, the LEDs of an infrared TV remote.

But they don't see it as IR. Instead, this infrared information just kind of irrevocably leaks into the RGB channels that we do perceive. With the unmodified camera on my Samsung phone, IR shows up kind of purple-ish. Which is... well... it's fake. Making invisible IR into visible purple is an artificially-produced artifact of the process that results in me being able to see things that are normally ~impossible for me to observe with my eyeballs.

When you generate your own "genuine" images using your digital camera(s), do you use an external IR filter? Or are you satisfied with knowing that the results are fake?

But the camera is trying to emulate how it would look if your eyes were seeing it. In order for it to be 'genuine' you would need not only the camera to genuine, but also the OS, the video driver, the viewing app, the display and the image format/compression. They all do things to the image that are not genuine.