Met a tiddly drunk, that cannot be denied (10)

I believe the answer is:

admittedly

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'cannot be denied' is the definition.
I can't tell whether this defines the answer.

'met a tiddly drunk' is the wordplay.
'drunk' indicates anagramming the letters.
'met'+'a'+'tiddly'='metatiddly'
'metatiddly' anagrammed gives 'ADMITTEDLY'.

'that' is the link.

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I've seen this clue in the Sydney Morning Herald.

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