not kidding at all. BTW: nothing to do with sensitivity.
It is not sensitivity, but noise. Increasing ISO will introduce luminous and chromatic noise. In most camera, noise won't show up in pictures until ISO reachs pretty high. But it is still there.
You are correct that aperture, shutter and ISO are linked. But aperture also controls the depth of field. Shutter control the motion.
The photographer takes a picture to capture an image, which tells a story at that moment, not just mathmatically corrected light exposure.