If this were true, then all people who observe the same training samples would learn equally well and predict equally well. But we don't. Some of us invent a better loss function than others or reject irrelevant data better. The representation formed by the data is surely derived, not fixed in its raw form. Forming a better representation of the data is the art of learning better. I'm convinced learning and remembering what you learn is more than kNN; in humans it involves data compression and recontextualization as you improve your loss function or tie your old representation to newly learned data — old raw data and representations that heretofore you had not believed were relevant to that objective (or lesson).