Every time the death bell tolls for Allofmp3 and the various iterations it spawns, another iteration pops up to take its place. While the Russian government has gone back and forth between leaving them be and shutting them down, the core group remains and continues to be a bone of contention between the U.S. and Russia.
While the site proper did finally get put into the dirt earlier this year, it is well known that they continue to operate with different names. As such, the U.S. is now asking Russia to hunt down and halt all the copycats as well, no matter who is operating them.
The assertion the U.S. is making is such that Russia not doing enough to prevent these sites from operating:
"Their refusal to use the technical tools at their disposal to staunch piracy exacerbates the problem."
That, in a sense, may be hypocritical. Piracy is a worldwide issue, not one relegated to a particular country. The issue is very similar to the U.S. stance on Internet gambling sites, where something illegal in one country is just fine in another. That led to the E.U. demanding cash from the U.S. due to lost profits. Technological cooperation has a lot of room for improvement, and would probably accomplish a lot more than demands another country get something done.