If I want to send a message to you, that only you can decrypt, I encrypt the message with your public key. Your private key is then required to decrypt it. If you want to send an encrypted message to me, you would encrypt with your private key and I would decrypt with your public key.
You have the first part right but using the if I wanted to send you a message I would use your public key to encrypt it not my own private key. If I use my own private key anyone in the world would be able to decrypt it via my public key. On the other hand if I used the recipient of the message's public key to encrypt only the person with his private key can encrypt (which is hopefully them).
Go to
http://en.wikipedia.org/wiki/Public-key_cryptography to brush up on your public key cryptography
Basically Nintendo is using a private key during manufacturing to encrypt the games, then decrypting at the console with the public key embedded in the console memory.
If this is true its the stupidest way of doing things ever.