Your pure logic is probably right; I do not have the time or interest to dissect it.

But you’re missing the context and implication: “doing new stuff” is the major achievement we’re looking for next from LLMs. Seeing something that is “new” and is not in the training set is interesting in a way that something contained in the training set is not.

We cannot introspect LLMs meaningfully yet, so the difference between “came up with myself and it’s in the training set incidentally” and “applied a concept in the training set” is not meaningful.