People should protect their networks, and most people do, but protected and secure are two different things, people used to think that FTP was protected because of passwords, but thazt doesn't mean it's secure.
As for the question of someone breaking into your network, and using it for illegal activity, then you getting blamed for it, to me, it seems to be akin to a guy running into a bar and shooting 3 people. Nobody in this situation would blame the manager, people would blame the perp. But at the same time, it would be expected that the manager take steps (eg, installing more cameras, perhaps a security guard on busy occasions) to help prevent it from happening again. The one problem with this analogy is that IT is so much more complex, it is entierly possible for someone to break into a network and leave barely a trace for a normal user to pickup.