Chin out - but not far (4)

I believe the answer is:

inch

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

'chin out' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'chin' is an anagram of 'INCH'.

'but' is the link.

Can you help me to learn more?

(Other definitions for inch that I've seen before include "Thirty-sixth of yard" , "Small Scottish island" , "Scottish island: unit of length" , "Short measure; island" , "Move in tiny increments" .)

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

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