Not true in the US due to compulsory licensing. [0] There's no permission required to publish or monetise a recording of an existing musical work - you just have to provide notice to the copyright holder and pay a statutory royalty. The mechanical rate for the sale of a recording is the greater of 9.1c for the song or 1.75c per minute of playtime. Streaming royalties are handled by blanket agreements with companies like Spotify.

[0]: https://help.songtrust.com/knowledge/what-is-a-compulsory-li...