Truly deep, possibly - or only ostensibly? (9)

I believe the answer is:

reputedly

I'm a little stuck... Click here to teach me more about this clue!

'only ostensibly?' is the definition.
I can't tell whether this defines the answer.

'truly deep possibly' is the wordplay.
'possibly' is an anagram indicator.
'truly'+'deep'='trulydeep'
'trulydeep' with letters rearranged gives 'REPUTEDLY'.

'or' is the link.

Can you help me to learn more?

(Other definitions for reputedly that I've seen before include "Allegedly" , "presumably" , "according to general belief" , "alleged" .)

I've seen this clue in The Independent.

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