That is only true if you define "stealing" to include depriving the original owner of the use of their property. Which almost nobody does.
"almost nobody" seems to include the US legal system: Dowling v. United States (1985) http://en.wikipedia.org/wiki/Dowling_v._United_States_(1985)
Copyright holders frequently refer to copyright infringement as theft. In copyright law, infringement does not refer to theft of physical objects that take away the owner's possession, but an instance where a person exercises one of the exclusive rights of the copyright holder without authorization. Courts have distinguished between copyright infringement and theft holding. For instance, in the United States Supreme Court case Dowling v. United States (1985), bootleg phonorecords did not constitute stolen property. Instead, "interference with copyright does not easily equate with theft, conversion, or fraud. The Copyright Act even employs a separate term of art to define one who misappropriates a copyright: '[...] an infringer of the copyright.'" The court said that in the case of copyright infringement, the province guaranteed to the copyright holder by copyright law—certain exclusive rights—is invaded, but no control, physical or otherwise, is taken over the copyright, nor is the copyright holder wholly deprived of using the copyrighted work or exercising the exclusive rights held.
Not to mention that in moral terms, it is the same damn thing as conventional theft. But hey, let's focus on technicalities of language. Nobody (except the industry people themselves, or those taking their paychecks such as legislators), is going to say that the tactics proposed by the media industry are reasonable or morally acceptable. But the fact that they are dicks about making their point does not diminish the validity of their point that piracy is not ok.
In moral terms, theft and copying are not the same thing. Taking a loaf of bread from you, or watching how you made a loaf of bread, and then going home and doing the same thing myself, are not morally equivalent. Even if you say two different things are both wrong, it's incorrect to assume from that, that they're necessarily the same wrong, in type or degree.