Minecraft did to inventories what most online games do out of the box these days. it put everything not critical to sim performance on the server. In the same way you can easily automate checks for speedhacks you can easily automate checks against this kind of behavior by authenticating player locations. The difference between starbase and a traditional servercentric model is that Frozenbyte isn't actually running the simulation servers, but they're still running central item, world state, and character data servers, and like any traditional MMO when a sim talks to the storage system there's usually a validity check in there somewhere.
Its basically just a really slow version of what all client/server games already do. When you move forward in an online game, you're telling you client "do the thing." and it says to the server "hey I did a thing"
In most online games the server then says "lemme check this thing you did to make sure its legit" and then sends back your new position, inventory, etc. to the client. This is why every game isn't full of item dupes and speedhacks. Your auth server's responsible for knowing the rules of the game and being able to tell when an action looks fishy (for example, 1000000 tons of ore appearing in an inventory without leaving another inventory with no rocks nearby)
The simulation may not be running on the auth server but all the economy and player account data is. Warframe and several other MMO-lite games use exactly the same system. Player clients host every game of warframe, but DE's servers house and authenticate all of the persistant economic, storage, customization, and progression data. Its a pretty well known implementation at this point, though nobody has tried to tie it together to distribute the load of a single persistant universe before, but I get where frozenbyte is going with the idea because it makes a lot of sense.
The secret sauce of starbase will have to be to smoothly transition players between two client nodes in some form, perhaps by using FBs in house servers as a bridge. This is where you see most games that use this approach being weak, if the host drops out everything screeches to a halt as the game slowly sends a snapshot of the current game state, selects another client, and then puts everyone back in place on the newly selected simulation. My assumption here is that Frozenbyte's trying to use in house resources to make that transition smoother, essentially using high performance in house servers as a bridge or a distributed computing mechanism to solve that problem.
If it works well, its a pretty revolutionary trick for running MMOs on the cheap and I'd love to see a whitepaper on the specific implementation. Done well it could actually make the central server model obsolete. Done poorly it could be annoying to play the game but not so much its a dealbreaker. I'm sure everyone would deal with occasional world freezes in exchange for everything else starbase offers.