I think you are underestimating the brain's ability to "fool itself" into thinking something is real if it's similar enough..
Not at all. It's a fantastic ability that gaming makes use of in countless ways - and
it's also why controllers with shorter response times will always be more immersive. There may indeed be a "psychological advantage" to motion controls for someone who's never ever used a normal button controller before, but the brain's ability to re-train itself means that once you're used to using a button controller, the initial awkwardness is gone, and you're left with pure muscle memory and
drastically shorter delays between thought and action - and thanks to the brain's ability to "fool itself," (yay, imagination,)
once you're used to it you won't notice the difference. To quote from the same article:
It takes a little while to get used to it, and figure out what buttons apply to what actions, but hey, it took a while for you to learn how to read, too. Motion controls, meanwhile, are thought → large movement → however long it takes for the console to register that movement → action. It's not immersive, it's going in completely the opposite direction to being immersive.