Public key decryption? 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.

Specifically this: 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.
Indeed the text quoted is wrong; at the very least, by using incorrect vocabulary. That should be: if you sign a message with your private key, the paired public key can be used to verify the signed message's integrity and origin.
What small amount of truth there is in the original statement boils down to: in some asymmetric cryptosystems, including RSA¹ (but not including ECDSA used in bitcoin and many other protocols), the sign operation includes a step similar to a step used in encryption, except with the private key instead of the public key; and that's undone in the verify operation, which includes a step similar to a step used in decryption, except with the public key instead of the private key.

¹ And then not the variant of RSA most used in practice for performance reasons, which uses the Chinese Remainder Theorem in private-key operations. That has no equivalent for public-key operations, and uses the private key in a form that makes it not interchangeable with the public key. That makes the twist in the text quoted unworkable.