The core of the comet has material undisturbed since its creation billions of years ago-- presumably. By examining the crater and ejecta, I'm guessing they can make an educated guess about what it's composed and perhaps how it was formed and, remotely, a stab at its age.
Right; I'm with ya. I read up on it and they didn't just smack the comet for the pure hell of it. They had cameras and gizmos to measure the content of the cloud, all kindsa' stuff.
I'm listening to the second half of the show right now :) First chance I've had to sit down and listen.