Source for this? I've heard it said a number of times but haven't looked into it. It makes sense, but I know many countries have laws about possession too.
Someone uploading a file, or downloading a file on a peer to peer website that also involves uploading a file is violating a number of these rights. Downloading a file(not on a peer to peer site) is not a violation of any of these exclusive rights. This is analogous to an unauthorized public screening of a movie. The the person who displayed the movie without permission is infringing on the rights holder's copyright, the people who are watching are not.
For instance, let's say the bittorrent protocol was altered such that instead of pieces, you're assigned random bits to upload that are never enough to be assembled into any part of the original file in human watchable form. Have you actually violated copyright if you upload some of these bits?
Eg what if you uploaded a single bit (a 1 or a 0). Clearly not in violation. How many bits do you need to upload to be in violation?
But even if you only seed while downloading it is likely even the relatively small amount uploaded would meet the legal requirement, the law does not require that you distributed a full copy of a particular work. Ultimately whether a specific amount would be enough would come down to the judge or jury.