Cite terrible periodontitis, refusing pie, though it's a twisting of the facts (10)

I believe the answer is:

distortion

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'twisting of the facts' is the definition.
'distortion' can be an answer for 'twisting' (synonyms). I'm unsure of the 'of the facts' bit.

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Another definition for distortion that I've seen is " A twisting out of shape".)

I've seen this clue in The Irish Times.

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