No, individual people downloading the occasional file aren't the cause of SOPA, nor are commercial pirates, for that matter. The cause of SOPA and its ilk is simply that the entertainment industry used to have a monopoly which became unsustainable the instant the internet came into existence, and are fighting tooth and nail to slow down or prevent the inevitable. They don't honestly care about pirates -- or at least the ones that know what they're doing don't. It's a front to keep up a veneer of legality, as well as to make the shareholders happy that their employees (yes, business executives are employes, not usually employers) are doing what they can to further maximize profits that are already maximized under the old business model -- which nobody wants to be the first to break away from. What this stuff is really about is preserving the stranglehold on distribution.
The recording industry has long enjoyed a world where every few years they get a new distribution format, which requires their customers to re-purchase their libraries. The internet is ultimately the end of that business model -- even with legal digital distribution schemes, physical medium is no longer an issue, to say nothing of illegal copyright infringement. This also says nothing of the fact that the internet creates a true global market (so no more exorbitant rates for countries that these cartels randomly decide can afford it), or any of the other myriad changes the internet made to the world. Basically, the internet has destroyed their business model, it has whether piracy gets completely shut down or not, and they're trying to intimidate the denizens of the web into not recognizing that. They've already lost the battle for hearts and minds, and they'll lose the overall battle in the long run, but it's going to be a while until the law catches up to technology -- like, say, 40 years or so for the millenials to finally take over for both the baby boomers and the gen X-ers.
Edit: Oh, before someone tells me "well, if there was no piracy, they wouldn't have that scapegoat!" -- you're right, they wouldn't have that scapegoat. These people are fully capable of cooking up a scapegoat for anything they want to do. If piracy didn't exist, they'd turn to child porn, or drug sales, or wikileaks, or any other thing on the internet that they could get people mad enough about to slip what they actually want done by in the name of preventing the scapegoat from happening. Heck, look at the games industry: piracy has been minimized as far as it feasibly can be. So what did the industry do? If you said "feel good about their record profits and stop trying to get even more control over the industry[footnote]and they really have been posting record profits in a down economy, despite all the complaints about piracy killing the industry[/footnote]", you'd be wrong. They started going after the used market, something that was completely legal but they could apply the same spurious logic to that they did piracy. This is not surprising. The surprising thing is that so many people bought it, instead of going "wait, if used games are worse for the industry than piracy, doesn't that mean that piracy is actually good for the industry?[footnote]Note to mods: I did not say that piracy is actually good for the industry. It's just that used games /are/, so logically, if used games are worse for the industry than piracy, either piracy is a great thing for the industry, or it's not, and they're lying when they say used games are worse.[/footnote]"