If you didn’t notice, the Tenth Circuit declined to grant a motion to file an amicus brief drafted by Sarah Krakoff and signed by several American Indian law professors in the HRI case. The court wrote:
Pending before the court are several motions seeking leave to file amicus briefs. Because the movants possess an adequate interest and present arguments that are useful to this court, we grant the motions of the Pueblos of Santa Clara, Sandia, Isleta, and Zia and the United Nuclear Corporation. We deny the motion of the American Indian Law Professors for leave to file an amicus brief only because granting the motion would cause one or more members of this court to recuse themselves from the matter. See 16AA Charles Alan Wright et al., Federal Practice and Procedure § 3975, at 318-19 (4th ed. 2008) (“Some circuits will restrict amicus filings in order to avoid disqualifying a member … of the en banc court….”). The states of Colorado, Kansas, New Mexico, Utah, and Wyoming also filed an amicus brief, which Federal Rule of Appellate Procedure 29(a) allows them to do without requesting the leave of this court.
Other than this oblique reference to Wright and Miller, there is no explanation for why one or more judges would have to recuse themselves from this matter.
Very troubling (but at least the Pueblo brief was accepted).
Turtle Talk 
They gave the explanation. Members of the court would have to disqualify (as adjunct faculty with professors wishing to file the brief). On a 6-5 decision, neither side could afford to have judges recuse. Pretty obvious.