The most common and most likely answer to this crossword clue is the 6 letter word MYTHIC
I've seen this crossword clue in The Daily Telegraph
M
Y
T
H
I
C
Buddy explains!

The straight part
We know that "Not true" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not true = mythic.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does MYTHIC mean?
MYTHIC adjective- Mythical; existing in myth.
- Larger-than-life.