Possibly, but they don't strike me as smart enough.
Maybe that's part of their plan!?
GlaxoSmithKline's involvement would be covert, of course. They'd slip a few bucks to a viral marketing -- I mean, political action committee. The PAC would whisper to the "family" groups, "Hey, I heard the FDA and CDC approved the quadrivalent HPV vaccine without testing it for effectiveness or safety! And Governor Perry called your daughter a slut!" And then things kind of snowball from there. We're not seeing actual GSK employees, or even employees of their employees ... just the foot soldiers inspired by their secret campaign.
Hey, if the tinfoil crowd can invent conspiracies about wide-ranging secret tests on our virgin foster children intended to give them autism or ... promiscuity ... I can invent conspiracy theories, too.