"Distillation" literally means to separate and take some components out of something. You can distill how a model works from a model. You cant distill a model from information because the information does not contain the model.
People are happy to conflate distilling with building because they dont like how the information was used. You distill how the model works from the model, and you build a model with information. Both could be morally good or bad but its not the same thing.
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.
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.