Sorry, but the monkey that does the scanning is kind of busy at the moment. Try again later!
PS: Updated the common portscan description. Also, feel free to get in touch and make it better / more useful.
The central concept of the packet-switched internet is that network nodes forwarding the packets (called routers) are just dumb packet forwarders and invisible to the communicating parties. It's called end-to-end transparency and it's what has enabled new Internet apps to be deployed without requiring support from the network. Like the web, or voip, or bittorrent.
http://tools.ietf.org/html/rfc1812#section-18.104.22.168 specifies what routers do when forwarding IPv4 packets.
Here are various other kinds of middlebox devices that are also generally about connecting networks at layer 3 with various side effects vs routing (just like NAT):
None of these devices are internet routers. It's just wrong terminology.