[foodstances]

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).

[Retric]

That does not require an open port on the printer connecting to the public internet. https://support.google.com/a/answer/3179170?hl=en

Is Port 5222 required inbound for the print server? No, only 5222 outbound is required.

443 TCP (HTTPS), with connections to: https://www.googleapis.com/* https://accounts.google.com/* https://www.google.com/cloudprint/*

5222 TCP (XMPP, using STARTTLS), with a persistent connection to: talk.google.com

[kieranmjones]

Well I did not know that, presumably that doesn't need port forwarding and is the printer communicating out rather than open ports onto the web?

[RIMR]

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...