The text of the law: "the service provider
responds expeditiously to remove, or disable access to, the
material that is claimed to be infringing upon notification
of claimed infringement as described in subsection (c)(3),"
They are also required to restore it if they receive a counter-notification and the issuer of the original takedown notice has not filed a lawsuit in 10-14 days. This implies they can not delete the file from their system and still meet their legal requirements.
Correct me if I'm wrong, but if I understand the text of DMCA correctly, they are not required to restore the content which was taken down, only that they may.
They are also required to restore it if they receive a counter-notification and the issuer of the original takedown notice has not filed a lawsuit in 10-14 days. This implies they can not delete the file from their system and still meet their legal requirements.