Public key decryption?
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.