Just because you don't have smartkey doesn't mean you don't have the alarm enabled.
A dealer can enable the alarm, but may instead try and sell you the alarm package. He is supposed to do that. They can use the scanner, go to Option Setup, then DOP Security, ON.
As long as they don't install GBS, DOP Security will be an option they can turn on.
If they do install GBS, then they have to remove or cut a specific wire to the Body ECU.
If you are lucky your dealer will do it for free. If not, ask if you can pay shop time for the tech to put the scanner on and make the adjustment in software.
Assuming you get them to do it, either for free, or for shop time; before you pay, be sure to test the system, according to the process in the manual. That way you can make sure they have activated the alarm.