I know the keys are random but have been linked together. This is proven by visiting ethereum database found here and here. I have confirmed several public and private keys at myetherwallet.com (with and without balance, including my own -- all are a match).
So my next question is.... if you cannot obtain a private key by only the public key, how was the database type websites created above? Why is the info on the site accurate? I have noticed the only thing searchable is private keys, not public key.