I think thats an oversimplification.
When talking about the Pirate bay, yes the topic of piracy is discussed. But it was not the Pirate bay doing the pirating, or offering the media themselves. What they did was to provide pointers to material that were hosted by others, and then downloaded by another, which for a long time was all perfectly legal in Sweden. A point that was lost to many lawyers from the US and UK who would quote laws like The Digital Millennium Copyright Act, only for the owners to mock and poke fun at them and point out US laws don't apply to people in Sweden.
However it is the thin edge of the wedge, obviously they knew exactly what was going on, so this became the new measure of if a company should be reigned in or not, Megaupload and other torrent sites are being targeted now, as apparently they should have know their sites were being used for file sharing, but where does this stop, is DropBox next, Youtube maybe google will be punished if it lists a copyrighted work in a search?
Regarding your claim copying is not stealing, technically you are right, it is copyright infringement. You can see Dowling v. United States (1985)
for more information behind that logic. Despite the RIAA and MPAA wishing it was so, and telling its audience copying is stealing, it is not. If it was, it would be a criminal offence not civil, as it is, they have to do the legwork to protect their material, if it was criminal, they could call the police to do so at taxpayers expense.
Right now they are pushing for more laws using legislation like sopa and acta, and so far they have met some resistance, but just like jason voorhees they will never give up. so expect new attempts, and if they fail, more attempts and unfortunately, politicians like to suck up to corporations that have made political donations, so I don't think they have been or will be looking for a fair deal for the average citizen of any particular country.