How does blockchain.info access my wallet in MyWallet I made a wallet at blockchain.info and enabled two-step authentication using Google Authenticator.

As I understand it, the operator of blockchain.info cannot access your wallet (unlike e.g. MtGox). Yet somehow blockchain.info can deposit coins in my wallet. 

Also, I assume the two-step does not work for the offline backup files, but the password does?
Your wallet is only used to send coins. To receive coins you don't need access to the wallet.