I am confused about the fees for storing files. What is to stop someone from modifying the code to just insert files for free? From what I understand there is nothing in the algorithm that would actually prevent that.
This will be rejected by the network. If everyone gets the 'modified' source, it will be possible, but it will not happen. So no one should use unchecked source . You can add some hacks to bitcoin client and get 'verified' transaction, but all other clients use correct software, so your transaction will be rejected.