Actually, he's half correct.
Each network card has a "unique" identifier called the MAC address. When connected to a network the MAC address is assigned an IP address. There can only be one network card on each IP address on the same network. However, with the magic of something called NAT (Network Address Translation) multiple people with different IPs on one side of the NAT gateway (a.k.a. router) can use the same outwards-facing IP.