The 'record' is a tangible and official document. They admit 'off the record' that the crime exists, but as there are no formal complaints there are no recorded figures.
'Off the record' is a device whereby people in the public eye give information to journalists without admitting that they are the source: when a politician says 'can I speak to you off the record?', a journalist can't say 'Gordon Brown's office said...' but has to say 'sources close to so-and-so...'. Your quote has some of this sense of 'off the record', but the main point is the lack of any official figures. If nobody reports the crime, the police can't say whether it's a growing problem.
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