They mightn't have direct say, but the army would still be beholden to them (being on the "right side") under the current legal understanding. Of course, when the AI army takes over what we know today isn't apt to hold much water. A coup, as we established, is very plausible. However, as you cannot predict the future it isn't unreasonable to try to place the bet given what you do know. That's all you can really do. If you end up on the losing side in the end you'd also still be on that side if you didn't act at all, so why not take the chance if you believe one of these companies will eventually take all? The AI army, once it starts seeking all, is going to come and take your resources anyway.