Happy carol turns out not to be authentic (10)

I believe the answer is:

apocryphal

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'to be authentic' is the definition.
Both the answer and definition are adjectives. Maybe they are linked in a way I don't understand?

'happy carol turns out' is the wordplay.
'turns out' indicates anagramming the letters.
'happy'+'carol'='happycarol'
'happycarol' anagrammed gives 'APOCRYPHAL'.

'not' acts as a link.

Can you help me to learn more?

(Other definitions for apocryphal that I've seen before include "probably made-up" , "Fabulous" .)

I've seen this clue in The Globe and Mail.

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