Incorrectly reported: it should be “Overlooked collecting rubbish” (9)

I believe the answer is:

misstated

'incorrectly reported' is the definition.

'overlooked collecting rubbish' is the wordplay.
'overlooked' becomes 'missed' ('miss' can be a synonym of 'overlook').
'collecting' indicates putting letters inside.
'rubbish' becomes 'tat' (I've seen this before).
'missed' enclosing 'tat' is 'MISSTATED'.

'it should be' is the link.

(Another definition for misstated that I've seen is " Set forth wrongly".)

I've seen this clue in The Independent.

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