It rusts just like iron, but the rust (AlOx, or alumina) stays bonded to the metal and actually protects it.

Rust being literal Fe2O3 makes a convincing argument that aluminium sure oxidises but doesn't rust pretty much by definition ;)

In other words: it rusts, but it doesn't rust like iron. It rusts in a much less destructive way because the aluminum oxide protects the rest of the aluminum from oxygen