Of course if you do it to everyone, total gridlock ensues and nobody gets to the place where they would be killed. If you only do it to a few, maybe there will be a handful of killings before everyone learns not to trust a text ever again.

As an aside, I agree living in a country where people will take their guns around and try to solve things vigilante style instead of calling the police, is a very bad thing in general. In all first-world countries except one, and in almost all developing countries in the world, this is a solved problem.

An AI might be able to run this attack against the entire planet, all at once.

Try to think like a not-human, and give yourself the capacity of near-infinite scale. What could you do? Human systems are hilariously easy to disrupt and you don't need nukes to make that happen.