Hi, Caspar! Sorry for the delayed reply – lots going on this week.
You’re right, if it’s going to your phone, there’ll be internet involved.
A friend of mine years ago had a system set up with a camera that came on when the door was opened. It immediately called his phone and he could watch whatever was going on in his house. (This was during a bitter divorce and custody battle.) We actually watched his mother in law plant something in his home from 3 states away. Of course, back then, we weren’t so worried about cameras inside our homes.
There has to be some kind of intrusion alarm that can link to a cell phone number.
This Simplisafe one seems pretty well encrypted. It might be worth checking out.