Viacom wants the data to prove that infringing material is more popular than user-created videos, which could be used to increase Google's liability if it is found guilty of contributory infringement.
I don't see this happening. Youtube may have a lot of copyrighted materials, but user-created videos have exploded.
Just a few of the smaller but popular examples:
Chocolate Rain -- 25,053,011
Leave Britney Alone -- 21,145,310 (and most of Chris Crockers other videos have an average of 2 million views)
Charlie the Unicorn -- 25,680,981
And of course, the king... Evolution of Dance, with 90,944,416 views.