said by Cyron :

While they may have the complete file, they didn't download any of the file from the person being sued. They're matching the hash from a verified source and then just look to see if you have a file with the same hash.

For P2P networks that don't hash files, they're just looking at the name of the file being shared.

said by Just The Facts:

The RIAA and MPAA have NEVER, EVER, EVER, EVER FILED A CASE OVER DOWNLOADING music or movies. They are filing against people offering/serving/allowing downloads. They have all the evidence neccessary to prove the transaction. It is the RIAA that is downloading the copyrighted material. They have the IP of the account serving the material, a time/date stamp of the transfer (to the RIAA), and the complete file. The only thing they can't prove is the actual person who allowed the serving. They do have the account owner and they are legally responsible for want is on/served from their computer so it is usually a slam dunk.

said by SRFireside :

You can stop uploading by moving the files from the default download folder of the program into something else. Most P2P programs give you the option of picking which drives, folders, files you want shared to the world. The program also creates its own folder to store the files you downloaded. While you can tell the program not to share any of your own files or folders it will always share what you download. So all you need to do is move the files from that download folder.

It's a little chore, but if you want to just download and not share anything that's the way to do it.

said by SRFireside :

Not if you move the files you just downloaded off that folder. If they are not in that folder they are not automatically shared.