Then when OpenAI does another training run it can also internalise that knowledge into the weights.
This is much like humans - we have short term memory (where it doesn't get into the internal model) and then things get baked into long term memory during sleep. AI's have context-level memory, and then that learning gets baked into the model during additional training.
Although whether or not it changed the weights IMO is not a prerequisite for whether something can learn something or not. I think we should be able to evaluate if something can learn by looking at it as a black-box, and we could make a black-box which would meet this definition if you spoke to a LLM and limited it to it's max context length each day, and then ran an overnight training run to incorporate learned knowledge into weights.
You didn't teach it, the model is still the same after you ran that. That is the same as a human following instructions without internalizing the knowledge, he forgets it afterward and didn't learn what he performed. If that was all humans did then there would be no point in school etc, but humans do so much more than that.
As long as LLM are like an Alzheimer's human they will never become a general intelligence. And following instructions is not learning at all, learning is building an internal model for those instructions that is more efficient and general than the instructions themselves, humans do that and that is how we manage to advance science and knowledge.