here's the situation:

arm the Element with the remote, but only able to disarm alarm via remote; using the key in the door will sound the alarm.

Does anyone else have this problem? Or is this expected behavior? It seems like you should be able to get into the car without the remote...

It's expected behavior. Don't think I've ever owned a car that wasn't like this.

really? I don't have a lot of experience with this sort of thing; never had this before in any of my cars; however, if I'm not mistaken, my wife's Accord is armed by using the remote, but can be disarmed by using a key...

Also, in the user manual, it explicitly says that the alarm will go off if you try and open the tailgate with the key, but it doesn't mention that the alarm will go off by using a key in any other keyhole.