My understanding of how public/private keys work is a little different.  The sender uses the public key to encrypt and send the data to the receiver.  The receiver uses the private key to decrypt the message.  The two keys are related to each other because each can encrypt and the other decrypt the message, but they are used individually.

On secure E-mail, both sides have public/private keys.  First it is encrypted with the sender's private key, then it is encrypted with the receiver's public key.  The receiver has to supply a password that decrypts his personal private key, decrypts the message using that private key and then uses the sender's public key to decrypt the plain text message.