In the article How Does the Blockchain Work? the writer makes the following statements:
Since only you should be able to spend your bitcoins, each wallet is protected by a special cryptographic method that uses a unique pair of distinct but connected keys: a private and a public key.
If a message is encrypted with a specific public key, only the owner of the paired private key can decrypt and read the message. The reverse is also true: If you encrypt a message with your private key, only the paired public key can decrypt it. When David wants to send bitcoins, he needs to broadcast a message encrypted with the private key of his wallet. As David is the only one who knows the private key necessary to unlock his wallet, he is the only one who can spend his bitcoins. Each node in the network can cross-check that the transaction request is coming from David by decrypting the message with the public key of his wallet.
If you encrypt a message with your private key, only the paired public key can decrypt it.
Is it true that you can encrypt a string with a private key and only the public key can decrypt it? I was aware of the reverse, obviously, but this just doesn't seem right.