The reason why they miscalculated is a mystery to me, perhaps they have realized they have let this "internet" thing go way too far, they cannot control it anymore using controlled disinformation techniques, and this was one of their last attempts to stop this trend.
Yes, it's really that bad out there. But it's getting better.
That being the case, it's not entirely surprising that the BSA would support anything that appears to make copyright enforcement easier for them. Nor is it particularly surprising that some of its members would find SOPA in conflict with their other interests and request that the BSA adopt a more nuanced position.
I guess that's just not as much fun as some of the other conspiracy theories I see in this thread.
BSA lobbies on behalf of member companies. The member companies know exactly what they are paying for. None of them are in the habit of throwing money away.
1) The underlying companies of the BSA (incl. AAPL and MSFT) were not really in favor of SOPA to begin with, and the public attention has lead them to correct the initial BSA position.
2) The underlying companies of the BSA were in favor of SOPA, which is why BSA supported SOPA. But in the face of public backlash they are backpedaling, because it is not valuable to support a bill that will lose regardless.
The second seems much more likely.
So no. I imagine almost everything done by a group like this is with the explicit approval, if not at the request, of almost all their members. But by not having to put their name on it they get an out in case it blows up in their face.
This is my thinking:
These companies belong to different trade groups. They pay their dues, contribute opinions on different things, but mostly leave these groups alone and go on doing their actual business.
Meanwhile, the trade groups advance their own agenda, given a mostly free hand by their constituency, which again, has better things to do. The group doesn't actually do all that much that's useful, otherwise their staff would be working for real companies. But they shuffle papers around, undertake activities like, say, harass small businesses about software licenses, and generally look like they have a reason for being.
Then, occasionally, these groups will step in dogshit and have to field a bunch of phone calls basically saying "Why the fuck am I paying you dues in exchange for this bad press? Make it go away."
And then the offending group needs to walk back the cat as happened in this blog post.
Plausible? Is that how this works? The explanation with the most incompetence involved seems most likely to me.