In the US, it is legal not to log (the NSA will do it anyway).
One possible reason that logging could be made required by law is to assist in tracking copyright violators. But I am not aware of any US regulators proactively enforcing such logging policy on file sharing service providers (such regulators do exist in some other countries though).
However, a claim by a file sharing service provider that it does not log, that is not on its website but just made in response to a query sounds like blatant BS. The logging of HTTP requests (which include the IP and web browser name/version) is normally done by default out of the box; the service provider would need to put efforts to turn this logging off. Although they could genuinely do this to make their service more attractive (think of VPN providers having logging turned off), this would indirectly position them as friendly to copyright infringement, which could make them a liable party should serious violation occur (Megaupload was a good example). Therefore, there are good reasons to:
- Tell some curious prospective customers that there is no logging;
- Keep logging.