How the hell was I able to receive BTCs via an address I do not own?
As Murch says one possibility is that this address is in your keypool. Another is that this is a change address the client created. If you're willing to share the relevant transaction we may have more to say.

Owning an address means "being in unique possession of a corresponding private key". It's difficult to know if you're the only owner, but verifying you have a key is easy - ask bitcoin-qt to sign a message with this address.