BSA acts independently, but on behalf of it's members. BSA have proven themselves to be a bit nutty when it comes to infringement, so it wasn't surprising that they jumped on SOPA initially.
However, as above, it was already a stretch by the press to connect BSA's view point on SOPA to the idea that all BSA members unanimously supported SOPA.
This sudden change of face from BSA indicates that indeed the members have spoken up and they do not agree with SOPA, and that the entire thing was just a load of fuss to generate clicks.
Companies like Microsoft and Apple also have a significant amount at risk by this wayward legislation.