No two devices can have the same IP address--World Wide, so that claim is false.
To clarify, our public IP addresses are assigned by the ISP connection and is always related to the addresses it owns. These addresses get re-established periodically, unless you BUY a domain name for yourself.
The public address is connected to the front-end of our routers. The router then assigns a LAN address to all of our devices, and this is were we see our device addresses like 192.168.1.x and there are millions of these, but they can not be reached from the Internet - - they're call non-routable.