The pertinent section for us from lj_biz
*Fandom Someone asked that we specifically address this, so: Along the same lines as the previous bullet point, we're not going to "shut down" fandoms or RPGs just because a sponsor said they wanted them shut down. We find that idea repulsive. However, we are (and have always been) legally obligated to act if we receive complaints indicating that someone is violating copyright or infringing on a trademark. This is a long-standing practice; we *have* to do this to avoid getting into legal trouble.
That said, we also enjoy legal freedoms by not actively seeking this sort of thing out -- a sponsor can't ask us to search for all communities of a given fandom so they can report them to us. If they want to do that, they have to do it on their own; we can't and won't help with that. So ultimately, our existing policies on copyright and trademark aren't going to change if a sponsor is on LJ; if they want to report icons or screencaps, the copyright holder will always have a legal right to do so. We're neither going to encourage them to do that, nor are we going to discourage them, either. LiveJournal needs to remain neutral in this type of situation, due to existing United States laws. We still have to enforce these laws whether or not we have sponsored communities.
Translation, yes they will shut you down if TPTB asks.
Full post here.