> after that a wrongly programmed AI may just as well "spring to life and start taking over the world" few minutes later.
That's physically impossible. AI still needs to improve incrementally and this will take time and resources. We can consider such AI to act like a virus - it will need a host to grow - in this case computer resources. It will be limited by the CPU, network speeds, storage and power. If it grows too fast it will starve the host of these resources which in turn will slow down it's progress. Even if the AI starts on a supercomputer in some university somewhere and decides that it needs more power, most likely it will start by "infecting" other computers on the network. These computers will not be nearly powerful enough to add much to the current processing power of the supercomputer. Such invasion is likely to get noticed. Each infected node will not be another super intelligent being, but due to hardware limitations it will most likely be a software that's limited in scope and designed to propagate and control the resources, linking them with the main host. We can safely assume that restarting, or reformatting the drives will restore the node to it's non-infected state thus slowing down the "invasion". Why we can assume that? It will take AI long time to learn everything about every architecture and operating system and apply that knowledge. The AI that's hosted on a supercomputer will not be able to suddenly start rewriting its software, take over nearby nodes, learn everything about our world etc.
>You're assuming that AI will grow with us and necessarily reach the same value system we have (one we don't really comprehend ourselves, mind you).
No I'm not. Only thing I can assume is that if the AI is smart enough to figure out how "convert" humans to paper clips, it will be smart enough to understand that it's pointless. It may decide to use it's super intelligence to take over the world, and I can't argue with that.. But if it continues to make paper clips even if they are no longer necessary then by definition this is not AI, just a stupid replicator.