Even if something is not directly connected to, or reachable from, the net they can still be a issue.

Consider something like a network printer.

Convenient as heck, but if your PC gets compromised only for a shot while the attacker may have left a little surprise in the printer firmware. End result is that even after you fully scrubbed the PC the attacker returns because the printer is acting as a proxy.

More and more it feels like a no win situation, unless you physically unplug the router between each time you need to do something online.