Some kinds of data have to be recorded, eg for certain sorts of financial transactions in excess of a certain amount. But you could operate an anonymous email service or some other sort of service where you don't retain any records. Government entities have been aware of/monitored 4chan for years, for example, but I've never heard of any attempt to compel Moot to engage in harvesting or storage of data (by compel I mean via litigation or legislation, not some politician saying 'there oughta be a law' on the nightly news).

By all means correct me if I'm wrong.