Exactly it is that simple. The Bitcoin network has no concept of "ownership" only authentication. If one can sign a transaction with a valid private key they can spend the coins. If someone generates an address which produces the same public key as your address then they can spend your coins.
And what would happen with money that is transferred to an address that exists twice? would this money be doubled?
Why would it get doubled? It is the same address, only more than one person has access to it. It is like sharing your wallet with your brother or whomever.