Not all networks are susceptible to this, but if you can get a 1:1 copy, that's no different from bittorrent, limewire, or KaZaA. That doesn't seem implausible for text.
Napster was an easy litigation mostly because of intent. There was a document trail a mile long that the primary goal of Napster was to facilitate copyright infringement, although on paper, it could be used to share anything.
Cameras, xerox machines, and audio recorders can all be used for infringement, but aren't illegal since that's not their primary purpose. For even finer lines, see the Betamax case. You can also look at cases about different sorts of transformations and transmissions:
- I buy a DVD. It is transferred via USB cable from a DVD player connected to my computer, temporarily copied to computer memory, and then shown on my monitor.
- I buy a DVD. It is transferred via the internet from a DVD player in my data center, via the Internet, temporarily copied to your computer memory, and then shown on your monitor.
Can you see how these have nearly identical technology, yet different legally? If you ever take a law class, there are a lot of discussions about how to draw such lines (disclaimer: IANAL, but I've sat in on law classes before).
To be clear, I'm not taking a stance about where this ought to land legally. I don't know. But the analogy to bittorrent, limewire, or KaZaA is a faulty one.