Like Kent, part of what I wasn't understanding was the "changing the shutter speed" thing. I'll be repeating others here, but in AP mode you can't change the shutter speed manually; the camera chooses the shutter speed and will change it if you change the aperture to keep the same exposure (same EV). The only way to change the exposure from "correct" is with EC (thereby changing the EV) in either AP, SP, and auto modes. In manual, you can change anything you want without camera interference so you can over or underexpose however many stops you want (again, changing the EV).
You can change the aperture all day long in AP mode (or shutter speed in SP mode) and the EV will stay the same. You have to use EC.