It has the same average density, but doesn't produce the same gravity anomaly. If the submarine were a perfect spherical shell of denser and lighter sub-shells

It has the same average density, but doesn't produce the same gravity anomaly. If the submarine were a perfect spherical shell of denser and lighter sub-shells, everything would cancel out. However, they're not. They're essentially really dense blobs attached to much less dense blobs. You get a gravity anomaly due to the lack of spherical symmetry.