Do you think their findings might have been impacted by the fact that they're only looking at healed head trauma injuries? I do understand that it can be hard to tell if certain damage is caused by post mortem events, but still, could their methodology skewed things a bit?
If not, and they're correct, I guess it means that when you have strong state control the violence within the population goes down. That doesn't mean violence itself necessarily goes down, though. How much state violence was there, how many executions, how many people were enslaved for doing violence to others? Also, the state, in order to expand its borders, would be exporting violence.
Look at Germany under Hitler, or Russia under Communism, or Spain under Franco. I'm sure they were very "safe" countries in terms of being able to walk down the streets unmolested, but how many people were in prison?