Well, this is messy, but I think you might appreciate the details. I'll use the common Speedstream 4200 DSL modem as an example. When installed in the approved AT&T manner, the ethernet port delivers192.168.1.64 to the external router. The management IP address of the DSL modem is 192.168.1.1.
When connected to a typical Linksys router, the router also wants to use 192.168.1.1 as it's IP address. That's not going to work, and the DSL modem automagically switches to 192.168.0.1 and delivers192.168.0.64. (This is not 100% reliable, causes some odd problems, and is largely responsible for why Belkin and others are delivering routers using 192.168.2.1).
At first glance, this arrangement looks like double NAT. It is, but with a difference. All IP ports in the DSL modem are forwarded to the ethernet port, so there's no problem with incoming traffic not making it to the router. Were this a "real" double NAT setup, the first router (in the DSL modem) would NOT have any ports forwarded by default.
The catch is that you can only forward ALL the IP ports to one IP address. That means that the DSL modem can only do the NAT thing to one IP address, and therefore to only one device. If that device is a router, there's no problem. If you try to connect an ethernet switch to the DSL modem, and plug in multiple computahs, only one computah will work.
There's one other item that might be of interest. The DSL modem intercepts all traffic on the WAN (DSL) side destined to the management IP address (192.168.1.1). Normally, the external router is configured to send everything to the internet, except the IP's on the LAN side (192.168.1.xxx). If you plug 192.168.1.1 into the web browser, the router will send it to the internet, and the DSL modem will not respond. So, they violate some RFC, and trap this address, sending it to the local LAN side, and then to the management web server inside the modem.
The problem is that the 4200 seems to have a botched implementation of this undocumented feature. The later DSL modems work well, as do most cable modems. Older modems lack this feature and require a static route on the WAN side to get to the DSL modem management web page.