Private key and public key are factors in a two factor mathematical relationship.
So there can potentially be many (possibly infinitely many, I haven't tried to prove this) valid private keys for any given public key.
So I can see that, given the public key email@example.com, I can see that there could be potentially many private keys. I see how you could brute force selecting a private key that matched your public key, and I can see that, depending how the brute-forcing is done, it would not be determinate that an attacker also trying to brute force a private key from the same public key would not come up with the same private key.
What I can't see is how, if you have a message which unlocks with the public key, how you can tell whether it was locked with the 'authentic' private key or with an attackers' inauthentic private key.