The attacks on torrent sites have little to do with headlines and more to do with the reality that they are critical points in the distribution of information people don't want shared.
To many people the distinction you point out is meaningless.
This is still pretty misleading. TPB only hosts the .torrent file, they don't have any of the contents of the files being shared. They don't even run a tracker anymore! Any method of distributing a small file to a large number of people would have worked in the exact same way. The only thing TPB has that (e.g.) Google Docs doesn't is mindshare.
The .torrent file can list multiple trackers. If it includes TPB's old trackers, connections will fail but the DHT and other trackers usually manage just fine. In fact, TPB said that trackers are obsolete ("not up-to-date") and that everyone should just use DHT and peer exchange (PEX) instead of relying on centralized trackers from now on. Some people still use trackers, but it's not really necessary.
Is it any surprise that the fed is attacking torrent sites? Even a tech news site puts incorrect titles on its news articles.
He didn't upload papers to the Pirate Bay, he uploaded a 165kb torrent file to the Pirate Bay.
It may sound like semantics but it has real legal repercussions.