I'm pretty sure your switch is working just the same as everyone else with the chrome switch. I do think it is weird to have the green on all the time for parking light no matter if lights are on or off, but that is the same for everyone with the chrome switch. I didn't know the chrome switch also lights green for the fogs. I think that is good.
Essentially the switch position itself is a good indicator for off, parking lights on, and headlights on, so it is fine to simply light up everything when any of the lights are on. Then I think it is nice to have the green for fog, because it is not so easy to tell if the switch is pulled out.
I do like my non-chrome switch, without the green parking light all the time, but I'm pretty darn sure your chrome switch is working just like all of the other chrome switches. If it bugs you, get the non-chrome switch. It is less expensive than the chrome switch and I don't think you will ever miss the chrome.
Two others with a switch like yours