There are two parts to factorio multiplayer.
- The game listing and mod delivery servers. These are hosted and run by Wube.
- The actual games themselves. These servers are hosted and run by third parties or private people and range from dedicated headless servers to someone simply hosting a game inside the client.
Hosted games can communicate with the listing server so that they can be discovered in game from the multiplayer game list. When a player joins such a game, they might need to download mods which are downloaded from the mod delivery server. Hosted games might check connecting player identity, in which case they communicate with the listing server to check the person has a real account that owns factorio. Hosts that ban players might also forward this information to the listing server which depending on the number of bans and reason for the ban might allow Wube to issue a general ban for that user that hosted servers can choose to opt in to, a feature that helps to combat griefing. Lastly when you browse the mod list in game that is viewing mods hosted by the mod delivery server, which Wube controls.
Although the two services Wube provide help improve the multiplayer experience significantly, they are entirely optional. Game hosts could decide to opt out of the listing server entirely, with clients being able to connect directly to the server via IP address and whatever user name they like. Mods can also be installed directly by the player by placing the corresponding mod folder or zip file into the factorio mods folder in appdata bypassing the need for the mod delivery server. However, I do not think mods auto download from a hosted server in this case, they would need to be manually installed.
Servers like the game listing and mod delivery server perform licence verification duties. It is not possible to verify if a user owns factorio without them.