Yeah, these things happen. I had a faulty rs232 bridge card in my GE Concord panel, caused the alarm to go off and not respond to the keypad.
At least your system doesn't dispatch the cops... Fun times tearing apart a security panel when the cops enter with guns drawn... I had some explaining to do. All worked out in the end, but proof it doesn't have to be internet connected for things to go wrong.
If you ever worked in the security industry, false alarms are the only thing that ever happens with security systems. Rarely do they ever go off and some legitimate reason is happening...
Except when I wired a water bug up to a zone on my panel. That saved me 4 times when the sump pump failed.
Sirens are useless, alerts via text, push messaging, email (ideally with camera images accessible) are the way to go.
Heck most retail stores now just have silent alarms. I wish more houses did too.