It muddies the issue, but people acted against SOPA, which is surely what they're trying to tap into.

I doubt they'll miss a few people who don't appreciate the issues being conflated, if doing so gains them some of the anti-SOPA folks who are willing to act.

Even when it came to fighting SOPA, much of the motivated base was under-informed and dealing in half-truths, exaggerations, fallacious arguments, etc.

But it worked.