I imagine that corporate interests (records, movies) in the US and EU could collude to get a pirate site taken down if it had a .org, it would just be another tree to fall.
So far the US has not publicly tried to drop wikileaks.org, forcing WikiLeaks migrate to a TLD that is clearly outside US reach. Maybe they wouldn't want the bad press.
I'm wondering what is possible if I simply have a relationship with a reseller in the US (e.g. the one with the superbowl ads, or eNom), but my TLD registrar is outside of reach. I assume they could make the reseller drop the contract, or terminate it.
EDIT: This is wrong, see peteri's post.
.org is essentially the same as .com, owned by the US government and managed by Verisign.