A VPN is absolute anonymization of the user for all sites you visit. The VPN only encrypts the traffic between the VPN server and the user, changing your IP address and it is extremely difficult to get into this traffic. With VPN, all sites on the network will indeed be unlocked for you, but this has nothing to do with anonymity - it absolutely does not prevent you from being identified. Read our article About user identification
and our infographics Brodilla VPN vs VPN.