Yes - we train only on a subset of human communication, the one using written symbols (even voice has much much more depth to it), but human brains train on the actual physical world.

Human students who only learned some new words but have not (yet) even began to really comprehend a subject will just throw around random words and sentences that sound great but have no basis in reality too.

For the same sentence, for example, "We need to open a new factory in country XY", the internal model lighting up inside the brain of someone who has actually participated when this was done previously will be much deeper and larger than that of someone who only heard about it in their course work. That same depth is zero for an LLM, which only knows the relations between words and has no representation of the world. Words alone cannot even begin to represent what the model created from the real-world sensors' data, which on top of the direct input is also based on many times compounded and already-internalized prior models (nobody establishes that new factory as a newly born baby with a fresh neural net, actually, even the newly born has inherited instincts that are all based on accumulated real world experiences, including the complex very structure of the brain).

Somewhat similarly, situations reported in comments like this one (client or manager vastly underestimating the effort required to do something): https://news.ycombinator.com/item?id=45123810 The internal model for a task of those far removed from actually doing it is very small compared to the internal models of those doing the work, so trying to gauge required effort falls short spectacularly if they also don't have the awareness.

Also the geniuses get beaten with a stick if they don't memorize and perfectly reproduce the text they've read.

I'm not sure what point you are trying to make. Are you saying in order to make LLMs better at learning the missing piece is to make the capable to interact with the outside world? Give them actuators and sensors?