Of the specific standards, only two—one as to each justice—could conceivably be relevant. The one that potentially relates to Justice Kagan requires disqualification “[w]here [the Justice] has served in governmental employment and in such capacity participated as counsel [or] adviser concerning the proceeding or expressed an opinion concerning the merits of the particular case or controversy.” “Proceeding” is defined to include all stages of the relevant litigation.
In order to run afoul of that provision, Justice Kagan herself would have had to participate in her official capacity as counsel or adviser in the case at any stage, or expressed an opinion in her official capacity about the merits. Asked during her confirmation proceedings whether she had done so, she said no. Absent evidence to the contrary, there is no reason not to credit that denial. Statements of opinion to friends or former colleagues do not count here.
The one provision that could apply to Justice Thomas requires recusal if the spouse of the Justice is known by him “to have an interest that could be substantially affected by the outcome of the proceeding.” Under the applicable law, the “interest that could be substantially affected” does not include a rooting interest, which is the only interest hypothesized even by the justice’s critics.