I get it was over your head. Extremis was not Tony's invention in the comics either. It was essential the same thing, except in the comics he was injected and that's what gave him remote control over the armor, as opposed to the injected tech. Anyway, the effect was the same. And because of the effect, that's where the comic mk30 got the extremis name. And since iron man 3 was that comic story only adapted for the movie universe...that's where he got it.
You may not have understood it, but that doesn't make it wrong or out of place. He called it extremis instead of prehensile. Exact same thing. The armor wasn't effected by the extremis drug, only Tony, in the comics again. But the armor is called the extremis armor. So no, sorry, you are not "right". It's a movie based on comics, and in this case even a specific story. So if someone knows both versions and uses a term from one version to describe something in the other version it doesn't make them wrong, just because you don't know both. Just makes you less informed.