A counter point here is you're ignoring all the boring we all die scenarios that are completely possible but too boring to make a movie about.
The AI hooked to a gene sequencer/printer test lab is something that is nearly if not completely possible now. It's something that can be relatively small in size compared with the facilities needed to make most weapons of mass destruction. It's something that is highly iterative, and parallelizable. And it's something powerful enough that if targeting at the correct things (kill all rice, kill all X people) that it easily spills over in to global conflict.
The AI hooked to a gene sequencer/printer test lab is something that is nearly if not completely possible now. It's something that can be relatively small in size compared with the facilities needed to make most weapons of mass destruction. It's something that is highly iterative, and parallelizable. And it's something powerful enough that if targeting at the correct things (kill all rice, kill all X people) that it easily spills over in to global conflict.