I don't see that there was massive publicity at all.
Hmh? McCoy was arrested for using the word in public - because everybody else in the universe had already been warned not to! We never met a person who would not
have known about Genesis, the Famous Forbidden World Where Nobody Can Go And There's Nothing Interesting There, Now Move Along.
The Federation might have an interest in keeping secret what transpired
at Genesis. Nobody else would. Klingons would probably broadcast their version everywhere, and they would find a highly interested audience.
Granted, nobody would really know "how to cook" now that the Marcuses had been shut up and down, but everybody would have an interest in finding out. Including those UFP or Starfleet parties who did not yet know, as the defense of the Federation might one day hinge on knowing exactly what a Genesis Wave is.