I've never seen "unbendable" arm as a 'trick', just a mind/body state that is essential for the doing of aikido.
The term 'unbendable' itself does not correctly describe the end state that is being trained for. It is true that if someone is testing my arm using strength, then what 'they' feel is that my arm is un- bendable, but I can choose to bend it as I wish, therefore it is only 'unbendable' to them.
As for teaching it, I usually can get beginners to 'get it' within minutes. The hard part is to maintain this state under ever increasing dynamically stressfull scenarios, this does seem to take a long time to achieve.
I've not seen the Tomiki unmoveable arm demo, and have not tried it, I look forward to Mike's report back. It seems to go against everything that I (as an aikidoka) would naturally want to do, i.e. when being pushed at right angles at the wrist, I'd want to turn on the spot, not stay stationary.
I don't know about the Tomiki thing, but the 'unbendable arm' exercise you describe is easy for beginners because it is a trick. The action being attempted by the bender is largely being thwarted by the mechanics of the setup. In order to apply a force that will truly test the bendability of the arm, one would need to apply a force down through the elbow and simultaneously up and towards the bendee's body with the shoulder, while making sure the bendee was fixed to the ground in a horizontal plane. There is only so much pulling downward on the elbow the bender can do without also dropping his/her own weight, and hence his/her shoulder - the primary action required to bend the arm is self-limiting. Also, in order to bend the arm, the bendee's wrist, and hence the bender, is going to need to close the distance to the bendee's torso, which is being thwarted by the fact that the bender is stuck in his/her own feet at a fixed distance from the bendee, bracing to pull down and trying ineffectually to drop his/her weight.
By contrast, imagine a machine, in which the person whose arm bendability is to be tested is limited from moving in the horizontal plane by a fixed steel ring circling the middle of their ribcage - not clamped, just limited from moving more than a half inch. Now, to test their arm bendability, we'll set up two bars. One will be positioned inside the elbow set to move radially downward and toward their waist using the position of their shoulder as the rough pivot point. The other will be underneath their forearm, set to pivot roughly radially to the other bar, toward the bendee's head/torso. Each bar will be fitted with a pneumatic piston capable of exerting 5000 pounds per square inch. Do you still think any human that ever lived would be able to demonstrate "unbendable arm"?