I saw the show, and it wasn't very well done.
They were talking about people gaining access to your personal files (tax returns, bank statements, etc.), for purposes of identity theft, but not how it was done, or how to prevent it.
Most p2p programs, by default, give others access to all files on your computer, unless you go into the options and restrict the files you want to share.
Most people just install the program, and start downloading, without even bothering to check how the options are set up, and that's where the problem lies.
Anyone, on the filesharing network, will be able to access, and download, any files you have marked to share.
Once they have your statements, and tax returns, they know everything they need to know about you, and your family; Social Security #'s, home address, full names, account #'s, etc
While p2p networks have their uses, they can be a dangerous place to venture into, without taking the proper precautions.