Commissioning social science studies just to influence the Supreme Court

Conservative groups have, in multiple amicus briefs, cited a "scientific" study to try to influence the Supreme Court on its upcoming California Prop 8 and DOMA cases.  (h/t Zach Cook) This week, that study about "family structures" that purported to show that straight parents were better at raising children than gay parents ran into serious trouble.  The study that had already been debunked and repudiated by other academics. But it was revealed by Zach Ford at ThinkProgress that the study had departed from standard procedures for refereed journals that are designed in part to guard against conflicts of interests.  For academia, double-blind review in which neither the author(s) or reviewers know each others idenities, is the gold standard to verify the quality, accuracy, and originality of research.  Ford's article reviews that the study was manipulated at various points in the review process specifically to produce results that would "prove" that gay parents should not be raising children.  The ultimatel hope of the conservatives guiding and funding this study was that it would be proof to influence the Supreme Court on issues of gay marriage.

The notion that the Supreme Court would be influenced by a social science study is intriguing.  I suppose ever since the Brandeis Brief was introduced in Muller v Oregon (1907), lawyers and interest groups have endeavored to bring non-legal data to bear in legal cases.  The efficacy of this tactic, except in Muller and the now famous doll experiment in Brown v Board (1954), is in question.  Supreme Court justices, as smart as they are, are only trained in law.  They have no formal or systematic training in statistics, economics, or social science.  How on earth would they know which study to believe, especially in a contested area where studies with findings pointing in different directions can be found?  As a political scientist that also studies law, I almost never see law reviews cite social science studies.  Despite all the calls for interdisciplinary studies, there is very little cross-pollination of the disciplines going on.  Am I to expect that this pattern is broken at the Supreme Court?  Any social scientists with empirical data on this question of how often the Supreme Court cites social science studies?