Presumably, the paper of record didn't produce this cock-and-bull story (1,6,2,4)

'presumably the paper' is the definition.
I know nothing about this answer so I can't judge whether it can be defined by this definition.

'of record didn't produce this cock-and-bull story' is the wordplay.
I cannot quite see how this works, but
'of' could be 'o' and 'o' is found in the answer.
'produce' could be 'issue' (I've seen this before) and 'issue' is located in the answer.
'story' could be 'lie' (story can mean a fabrication) and 'lie' is found within the answer.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?