It is flatly impossible to straighten or bend the arm "without tensing the arm muscles at all". Tensing the arm muscles is what makes the arm bend or straighten. This is not only true with someone providing resistance but also when one is floating freely in a non-gravity environment. The arm does not voluntarily bend without the application of muscular tension on one side of the joint sufficient to overcome the resistance to bending, no matter how small that resistance is.
What I should have said is that there is no "discernible" tension. As I described in my earlier post, I can do this with a third person touching my upper and lower arm and they don't feel the muscles firing. I am not trying to upset anyone's notion of correct science, I haven't got the anatomy training to tell you what I am doing. What I am saying is that a) I can do it and do so all the time when I teach folks, so plenty of people experience it and b) the reason that I show this when I teach is that this skill, however minor, is crucial to doing any technique with "aiki". If you can't do it or don't understand it properly, your Aikido remains largely physical and strength based ie ineffective.
The whole unbendable arm demo is supposed to be showing the proper energetic state of the arms which is right in the state between pushing and pulling (or collapsing). Most of the folks who do it as beginners don't understand how to flex it, their unbendable arm is too rigid and isn't really what I am talking about nor is it what Tohei Sensei was demonstrating.