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Yes, a provider can follow the DMCA safe harbor procedures to facilitate the filing of DMCA takedown notices, and comply with those promptly. The details are outlined here: http://www.chillingeffects.org/dmca512/faq.cgi

Basically, a provider needs to provide contact information for a designated agent for DMCA takedown notices. Had Luke done so, and complied with legal DMCA takedown requests (as well as counter-notifications), he could have continued operating his service; however, that may have become considerably more work than he wanted to put into running the service.