Chris,
It's true that cores are swaged, but so are whole bullets. Take a look at the gray bullets on
this Hornady list, or at the Corbin bullet swaging site,
here.
TXGunnut,
They aren't all pure lead. Hornady or Speer used to claim theres had a couple of percent Antimony. Corbin sells pure lead wire, but he also has a calculator for figuring pressure for swaging different alloys up to about BHN 8-10.