Some of their familiar stories may not be believed (5)

I believe the answer is:

liars

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'not be believed' is the definition.
I can't tell whether this defines the answer.

'some of their familiar stories' is the wordplay.
'some of' says the answer is hidden in the clue.
'LIARS' is hidden within 'their familiar stories'.

'may' is the link.

Can you help me to learn more?

(Other definitions for liars that I've seen before include "Prevaricators" , "Deceivers" , "Untruthful people" , "Tellers of deliberate untruths" .)

I've seen this clue in the Evening Standard.

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