backing up 12 seed words vs wallet.dat
The seeds produce the addresses, not the balances.  Consider that you can have multiple wallets that contain the same address.  The balance doesn't exist in both addresses, because there's two copies ... it's like you said at the end.  

Your wallet looks up the addresses in the blockchain that's copied on your system, and they contain the balance ... well, actually, the balance isn't actually an entity.  The transactions are.  Your wallet scans the blockchain for your addresses, and any transactions that involved it, and calculates the balance based on the inputs and outputs.