This does not follow at all.
My roomba makes choices all the time. It does not have free will.
But the guy who chose the entirely deterministic and rule-based system which the roomba uses to "choose" one path over the other does, I would presume. If humans have such strict rulesets, we certainly don't know about them. It's math all the way down in the case of AI. There's nothing arbitrary about it. Even "random numbers" are generated with algorithms which return quite specific results... with time passing as the "randomizing" factor (but it's not random. Math is incapable of random).
But yeah... that goes back to my original point. You can't prove the non-existence of free choice within a system explicitly designed to remove all the free choice before you can calculate. All systems which we can sufficiently control to produce a result would qualify as inadequate in this regard.
Basically, instead of disproving "free choice" all you end up doing is proving the inadequacy of your method. You won't find it there. It literally can't exist within a mathematical framework. Probabilities are about as close as you can get, but they fail at actually producing an action in real time. We can produce an algorithm which mimics a probability, but each individual result is still entirely deterministic.
You can't prove "absolute internal control" by using external manipulation. It can only be detected within the system. Luckily for us, our consciousness is that system, and it's quite obvious until you go about trying to prove it to others. Of course, I'm assuming that all other humans are conscious. I can't prove that. I could very well be playing a single-player game where I'm the only entity which is actually conscious... but that heads us toward brain-in-a-vat solipsism.
I dunno... maybe your roomba IS conscious. But I would assume not if it always performs exactly as programmed. In a way, only the roomba can really answer that question, and there's no reason to take its word for it if it somehow communicates, because that could also be (is likely to be) entirely the result of external factors in the case of AI.
If it nearly always does what you ask it to, then it likely doesn't have free will. That's as close as I can get to an indicator, and that's not absolute. But it can really only be detected by eliminating external controls.