The rules don't require the person holding the content to scan the content. Normally a DMCA claim is issued before the host has to get involved.

Lets say you and I opened a joint safe deposit box at the bank to share USB drives together with movies on it. If the bank found out, they wouldn't be required to drill it open and scan the drive to make sure none of the movies were copyrighted. This is google drilling open the safe deposit box because someone shared the keys, and they think there may be a movie they don't like there.