From the Robertson, Bergstrand, and Winkelman brief in Lieu v. FEC:

Plaintiffs-Appellants have asked the Court to reconsider its decision in
SpeechNow.org v. Federal Election Commission, 599 F.3d 686 (D.C. Cir. 2010), which gave rise to so-called Super PACs and similar independent expenditure organizations. The Court in SpeechNow recognized that the “appearance of corruption” could justify campaign finance regulation under Supreme Court precedent. Id. at 692. But the Court went on to state that, “[i]n light of the [Supreme] Court’s holding as a matter of law that independent expenditures do not corrupt or create the appearance of quid pro quo corruption, contributions to groups that make only independent expenditures”—like SuperPACs—“also cannot corrupt or create the appearance of corruption.” Id. at 694. Amici’s empirical research strongly suggests otherwise. In two studies with complementary methodologies, Amici found that contributions to organizations that make only independent expenditures may in fact create the appearance of quid pro quo corruption. In light of this empirical research, the Court should grant initial hearing en banc and reconsider its decision in Speechnow, which rests on an incorrect premise.