Fellow broadcast to CID a dodgy bit of info (7)

I believe the answer is:

factoid

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'info' is the definition.
(I know that factoid is a type of info)

'fellow broadcast to cid a' is the wordplay.
'fellow' becomes 'f' (abbreviation - of a society etc.).
'broadcast' is an anagram indicator (letters scattered or cast around).
'to'+'cid'+'a'='tocida'
'tocida' with letters rearranged gives 'actoid'.
'f'+'actoid'='FACTOID'

'dodgy bit of' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for factoid that I've seen before include "Dubious nugget" , "Unreliable information" .)

I've seen this clue in The Daily Express.

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