An IP address is not an end-all identifier.
The biggest thing that was able to be used for true identification was the Processor Serial Number introduced in the Pentium 3 line. Due to major privacy concerns, that feature got stripped out in the second-gen P4 line (first gen had the CPUID but you could turn it off.)
After all, you could just as easily use a cantenna and get wireless signal from another place a few hundred yards down the road, or setup a wireless repeater using an old router and DD-WRT firmware.