Strange... I tried my other keys, and it appears that the alarm will sound sometimes with all of them when physically unlocking the door. Even the new one can successfully open the door without setting off the alarm. Note that I'm not opening the door, just unlocking it by turning the key. So it seems like there's a problem with the theft deterrent system, and only the dealer can fix it?
Definitely sounds like a flaky switch in the lock, but I would not take it to the dealer they will try and sell you the power locking mechanism plus labor I would guess $600? I would squirt some WD-40 in the lock and work the keys a little bit but if it keeps doing it just avoid using the keys in the lock! You have three working remotes, right?