This is equivalent to the famous double-spend problem in designing decentralized currencies, except instead of the goal being to prevent a previous owner of a coin from being able to send it again, here the goal is to prevent the previous key controlling an account from being able to change the key. Just like creating a decentralized currency, doing account management in a decentralized way requires something like a blockchain. A blockchain can timestamp the key change messages, providing common knowledge over whether B or C came first.