Google's Cloud Print service (used on Chromebooks at least) has to constantly keep your printer in communication with the internet. To print to a printer on your LAN from a Chromebook, it goes out through the internet to Google's servers then back down to the printer. (And often times it stops working, so you can't even print to the thing 2 feet away).
There's a difference between being "connected to the Internet" and being "open to the Internet".
There are hundreds of thousands of printers, mostly at Universities, that can be installed just pasting their WAN IP address into the Windows "Add Printer" wizard...