Google needs more than actual knowledge that the video is a copyrighted work–they need to know that it is unauthorized or be "aware of facts or circumstances from which infringing activity is apparent". If they no longer have a formal relationship with the artist and no longer have the artist's original works to have the Content ID system compare to, then they have very few ways other than DMCA complaints to become sufficiently aware or certain of infringement.
What I find more interesting is 17 U.S.C. § 512 (i):
(1) Accommodation of technology. — The limitations on liability established by this section shall apply to a service provider only if the service provider —
(A) has adopted and reasonably implemented, and informs subscribers and account holders of the service provider's system or network of, a policy that provides for the termination in appropriate circumstances of subscribers and account holders of the service provider's system or network who are repeat infringers; and
(B) accommodates and does not interfere with standard technical measures.
(2) Definition. — As used in this subsection, the term “standard technical measures” means technical measures that are used by copyright owners to identify or protect copyrighted works and—
(A) have been developed pursuant to a broad consensus of copyright owners and service providers in an open, fair, voluntary, multi-industry standards process;
(B) are available to any person on reasonable and nondiscriminatory terms; and
(C) do not impose substantial costs on service providers or substantial burdens on their systems or networks.
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Thus, they don't have to provide Content ID themselves, but they have to allow for a third-party Content ID that doesn't have all the strings attached.