As I said, the money campaign makes an absurd equivalency between two things to bring attention to another absurd equivalency. It is not meant to prove anything but rather highlight the issue. (At least that is my take on it.)
"where exactly do they equate copying with physical taking anyway"
When they propose that acts of piracy equate to lost sales (and I'm sure I could find more literal examples when I have some time). While I do not condone piracy, there is no direct equivalency to lost sales, and any discussion of how to combat piracy needs to accept that.
I don't care much about semantics like the term "stealing" except when people try to use it to misrepresent an issue. I'm pretty sure the media companies are not using it like "stealing one's heart". Regardless, clear unbiased terminology (or a lack thereof) is not the biggest problem here.
The problem is that the media companies are not combating THEFT. They are combating COPYING. Copying in itself is not theft. Legitimate customers have good reasons to want to make copies, but the measures that media companies put in place to supposedly prevent piracy often hurt legitimate customers more than pirates. Pirates just break the copy protection and then end up with copies that are actually better than what PAYING CUSTOMERS get. As a paying customer, this is just about the biggest insult a company can lay upon me. Are they really trying to stop pirates or just trying to make my life more difficult? And it is not just a matter of "feeling" hurt. Real damage can result when companies use piracy as an excuse to push things like root-kit copy protection schemes, overly aggressive take-downs, and SOPA.
I'm no fan of places like pirate bay. It seems to me like the people running those sites are total scum and need to be put in jail for a long time. So let's focus our efforts on actually stopping thieves rather than treating everyone like criminals.