So, let’s say, if some recording artist at, let’s say, Jewish Music, Inc., by the name of, let’s say, JJJ, uses a Carlbach tune without permission, as his own, and now Jewish Music, Inc. says it’s assur to copy; that’s ok? (All names are made up).
JJJ (or Jewish Music, Inc.) is required to get a mechanical license from whoever owns the Carlebach portfolio. JJJ (or Jewish Music, Inc.) owns the copyright for the new recording.
Mechanical licenses are mandatory so whoever own the Carlebach portfolio cannot deny it to JJJ. Going a step further you can get a mandatory mechanical licence for any publicly released music. (Even music that was just released.)