The car's electrical system was designed that way; I wouldn't mess with it.
I know for a fact fog lights and high-beams are illegal in most states (why? I have no idea; makes no sense), so all auto manufacturers wire them to turn off, at least in the US. However, some cars allow you to turn the fogs on with the parking lights, like my GTO, but most Japanese cars I've owned didn't do it. I'm sure it could be done, but why risk frying something, or voiding your warranty just for that? Your call. Later.
Only way to do it is to rewire, can't use the stock switch as there is a relay system built into it. On my civic I rewired it using my own relay and the switch powered off of the cigarette adapter so that they turned on when the switch was on and only got power when the car was on. I just used a lighted rocker switch, a relay and good wiring with a 20A fuse, direct power from Battery. Most audio shops will even do it for you if you pay a guy on the side.