Viacom will lose
You miss the big trick. DMCA says Viacom needs to list the items it owns copyright to and ask for removal of them. Viacom claims it cannot do that because users can are allowed to have private videos (which it cannot search for) and allowed to have closed distribution lists of friends (which it cannot get access to, and presumably can't fake friendship to obtain access to).
The Judge can't go along with Viacom on that because email providers would be required to filter email for potential copyright violations, (also closed list of recipients and also private).
People with private servers would have to open them up for scrutiny for potential copyright violations, (also closed, also private). Viacoms own internal servers are accessible only to their own people and may contain other people's copyright material.
So that argument is a non starter.
"YouTube strategy has been to avoid taking proactive steps to curtail"
And seemingly Viacoms strategy is to not take proactive steps to issue a DMCA claim either. Something the RIAA does with automated software! If they did Google could (and does) 'suspend' the accounts.
Without that Viacom are left with a 'we can't find our clips fast enough', well if Viacom can't find them, neither can downloaders, so the copyright infringement isn't happening! If the people can find the Southpark clips then so can Viacom!
Finally the biggest problem with Viacoms argument is this.
ALL VIDEOS ARE COPYRIGHTED BY DEFAULT, and Google has no way of knowing who the copyright owner is, or if they approve of the upload, unless someone sticks in a DMCA takedown notice.
Google will win this one easy, but perhaps we can fair use codified as an added bonus if the claim covers snippets of copyrighted work.