Actually yeah, it's that simple. Like say you take some aluminum cans and melt them in your backyard. Some of the inks and plastics burns off from the heat. The oxides float up to the top and you can scoop them out. What you pour out after is basically clean aluminum. Big industrial process are bigger, but functionally the same. They just pay a bit more attention to not letting oxygen contact the molten aluminum to prevent unnecessary oxidation. There are still some non aluminum impurities that get in there so you can't make a lot of alloys out of it, but it's plenty fine for lots of purposes like aluminum foil and cans and stuff that aren't like making up the wing of an airplane.

The dross you skim out is mostly it's aluminum oxide, but also contains a large amount of metallic aluminum that followed along for the ride. Depending on the initial melt composition and handling it can contain anywhere from 15%-85% recoverable aluminum. That can be recovered by mixing it with molten salt fluxes. This allows the metallic aluminum to separate out while the oxides mix in with the salt in a separate layer. You get an even worse grade of aluminum out due to the large amount of flux used, but again it's still useful for lots of stuff and the whole melting process takes something like 90% less energy vs processing raw aluminum oxides. The extra contamination from the salt flux is why you don't just toss in a bunch of salt in the first place.

Afterward once the salt is loaded up so much that it isn't useful as flux anymore is allowed to cool and is pitched as trash. It's called salt cake, and is actually a decent bit hazardous. Disposing of it safely is kindof becoming a problem actually.