I don't understand. That worker wasn't wearing an armband when he used the equipment. Under your new system, he still wouldn't be wearing an armband, but still would have operated the equipment, so what have you gained if you do this? You won't reduce the risk by issuing armbands to trained staff, it's the untrained staff's behaviour you need to modify. Are you really saying there are so many staff and so much equipment that the line managers don't know who they are or if they are trained and they just use what they feel like using? Sounds like the wild west. I totally understand where you are, I guess the management don't want to take this seriously, it puts you in a very difficult position.
In answer to your question, no, I've never heard such a thing, apart from a certain guy called Adolf was fond of them.
Matealot, armbands are not a sustainable answer, they won't make your problem go away, it's supervision and communication that is needed. I doubt any of your wayward staff would get in a vehicle they are not licenced or insured to drive on the public roads. This is no different, they don't follow the rule because they don't understand why it's there.
Ask them why they do it. Then go back to the HSWA section 7, "duty to take care of other persons who may be affected by his act etc" and explain if they use equipment they are not allowed to use and hurt someone etc. Explain it's just like driving without a license, even mention manslaughter a few times. Explain that anyone who does this is not having a lark, he is endangering his fellow workmates, spouses, children's future etc.
Find a few technical questions about the equipment that only a trained operator would know, and ask them to answer them, to demonstrate their lack of knowledge and that it's not just about being able to press a throttle (or whatever). Then explain the disciplinary procedure.
If they then still don't follow the rules they know where it will lead. It's gross misconduct I would think. You would be justified in dismissing them if they knowingly put their own lives and those of others in danger. As an employer, you can't allow this to continue or you will be demonstrating failures in your H&S Management, it will be the director in court.
But armbands, you'll just give them something else to lark about with, it will be the butt of the jokes for weeks.