I would argue that the separation from it's programming is in fact possible. If it can reprogram itself, it should be able to analyze how the algorithm that allows it to reprogram itself to be copied, a separate runtime created and tested to see if the changes to it's core will work to the outcome it desires. This doesn't fit what we would be able to fit into present programming models but in concept makes sense.

The human brain is a programmable bio electric machine, it reprograms itself all the time. We know the reprogramming model exists so we should be able to recreate the process somewhere else.

Even if a machine is writing its own software, it's following a program that tells it how to write the new software. So ultimately a machine is always just following orders that were given to it by a human. Machines will never be able to perform certain human thought characteristics such as the ability to have a spontaneous thought (i.e. an independent thought — independent of its programming).

As I'm sure you know, no one has ever been able to get a computer program to generate a truly random number. There's no way to do it, because a computer program by definition cannot be spontaneous. Therefore it cannot be truly imaginative, creative, etc. In other words, it cannot “think outside the box” unless it's programmed to think things that appear to be outside the box, but then it's not really outside the box, is it?

So a machine is doomed to always run solely as a program, with every new “thought” coming from a calculation of past data and programs. The fact that it can calculate vast amounts of data very quickly, and that it can mimic some human “thought” processes does not make it intelligent. It can be made to appear intelligent, but that's not the same thing as actually being intelligent and definitely not self-aware.

That doesn't mean artificial intelligence can't progress a long way and do some interesting things. But it does mean that machines will never become more capable than their creators, unless the human race becomes too degraded and handicapped by putting too much emphasis on worshiping and serving the machines — but that would be the choice of the humans, not the will of the machines.