Soiled clothes are a private matter? (5,7)

I believe the answer is:

dirty laundry

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'a private matter?' is the definition.
I know nothing about this answer so I can't tell whether this works.

'soiled clothes' is the wordplay.
'soiled' becomes 'dirty' (synonyms).
'clothes' becomes 'laundry' (laundry is a kind of clothes).
'dirty'+'laundry'='DIRTY LAUNDRY'

'are' acts as a link.

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

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