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A letter to regret, as a matter of fact (4)

Ross

I believe the answer is:

true

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'as a matter of fact' is the definition.
Both the definition and answer are adverbs. Maybe there's an association between them I don't understand?

'a letter to regret' is the wordplay.
'a letter' becomes 't' ().
'to regret' becomes 'rue' ('rue' can be a synonym of 'regret').
't'+'rue'='TRUE'

Can you help me to learn more?

(Other definitions for true that I've seen before include "Right - honourable" , "In accordance with facts" , "Genuine, actual" , "Rightly so called" , "Veritable" .)

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