Key story that may not be true (6)
I believe the answer is:
legend
I believe this is a double definition.
'key' is the first definition.
(thesaurus)
'story that may not be true' is the second definition.
(Other definitions for legend that I've seen before include "Story of mythical beings or events" , "One always remembered" , "Tale of folklore" , "Inscription; myth" , "Former top player" .)