Alarm on a 2004 base

[dh271]

I`ve had Chevy salesmen and others tell me I should have an alarm already installed as standard equipment. I have the red panic button on my remote and it does work, but I have no alarm, which a salesman said if I had the panic button, then I have the alarm. The owners manual shows the setting for the alarm on the radio readout, but mine doesn`t have it.
My only question is, was the alarm supposed to be standard equipment or do others not have a factory installed alarm too.