> Information is information

Not really, what the information actually is, matters a great deal. It's harder to get good results going from "nothing > model+weights" than "nothing + traces from known good sessions of other good model > model+weights", this is what the "distillation" part is referring to. If "information is information", you wouldn't even need to separate good from bad sessions while doing the training, which leads to somewhat obvious results if you don't.

Can you be more specific? I have no idea what you are trying to say.

To succinctly restate my point, you cannot distill a model from information because the model is not contained within that information. You can distill a model from another model.