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).
In this line of argument, the host that houses the servers is also a third party. So, there's no need to contact the opperator, when they could just access the machines.
That doesn't mean some Federal agents haven't paid him a visit and told him to log IPs or else they might start "investigating" the site. If they want to the Feds could easily come up with grounds for seizing the sites hardware. I suspect moot "volunteers" information related to serious crimes.
It is notable that some 4chan competitors have gone out of their way to say they don't log IPs and have distributed their infrastructure.
By all means correct me if I'm wrong.