I was cognizant of the compusory license regarding live concerts but am not aware of one permitting recorded music. To my understanding the compulsory license involves only the "public performance" portion of a song's copyright, not the right to actually create, press and distribute your own version on a phonograph (CD). Whoever holds that portion of the copyright has to issue explicit permission - usually it's the record company, hence all the Countdown Singers dopplegangers and the appeal of independent labels.