Accessing clients across different subnets

I discovered that I can do something that seems to violate the IP protocol.

I have SBC as my DSL ISP. It sent me a Speedstream modem 5600 series. This modem has some quasi-routing qualities to it. When I connect my computer directly to the modem with everything in their default settinngs with the PC being told to obtain IP address automatically, the NIC gets a public IP like 68.10.10.10 and I can get out to the Internet.

But then when I type in 192.168.0.1 in the browser, I see the configuration screen of the modem where I can choose to let the modem to act as a router of sort. Basically I can tell the modem to act as a NAT router. This way, the PC will get a private non-routable IP like 192.168.0.2. Here is the confusion. I should not be able to connect to the modem at all at 192.168.0.1 in the first place because at the time of the connection, the NIC has a public IP like the aforemention 68.10.10.10. But I can. Why?

All this seems to violate the principle of subnetting when a NIC of one subnet (my PC) should not be able to see another NIC on another subnet (the modem).

 

The 5600 series do contain a fully functional router and has some pre-set route tables set up in firmware so the user can't change things.

It's doing some internal stuff to allow that connection. The 192.168.x.x addresses by design are not normally routable but it's possible with the right settings.