As a former broadband network architect (Telocity/Directv DSL) my understanding of modern Cable and DSL provider use of the term "modem" is that Modem implies a tunneled link between the CPE (Customer Premise Equipment) and a box at the ISP.
So here at my home using Comcast, we have a CPE Cable Ethernet/Cable COAX proxy that gets a outward facing DHCP IP from a server at the local Comcast ISP. This IP is part of a private non-Internet network. The CPE/Proxy then connects to a server at Comcast's data center using a PPTP tunnel, authenticating (customer-side) using keys stored in the CPE and (server-side) with a database of current active paid customers.
If authentication completes successfully, then the CPE Device links the PPTP tunnel to my local network and to the real internet on the far side of the multi-interface ISP Server.
so it's more like:
_______________{------- PPTP tunnel ------}
PC-- local net -- CPE -- ISP Private net -- ISP Server -- Internet
This is much more like a real telephony modem than a router or network type converting Gateway.
The reason they use this is of course now all they need to do to cut you off is change the ISP Database if you don't pay your bill.
If the real Internet was run out to your house, you could just run your own CPE and get free service until they sent a Tech to unwire your link (or have smarter more expensive hubs that can remotely cut-off links). That's too expensive to be cost effective, so they use the "modem" model to control costs. They usually make you pay for the CPE too so it's really a net gain.
Interestingly, this is why rebooting your CPE "modem" often fixes broken Cable Internet connectivity. It forces it to connect out to a new PPTP server and if the ISP PPTP server being broken/overloaded is the issue, then you have a whole new one and it tends to work better.