Yes, inherent power does reach that –

After an investigation by special master Louis Freeh, the district court administering the Deepwater Horizon claims process imposed sanctions on a law firm that had exploited a relationship with a former staff attorney for the program. Among other arguments, the firm argued that the district court could not invoke its inherent power, because the program was not a court proceeding. The Fifth Circuit disagreed, noting that the district court had retained jurisdiction over administration of the program in the order that created it, so its “inherent authority to police seroius misconduct before it extended to the [program] over which it retained continuing and exclusive jurisdiction.” The Court distinguished Positive Software Solutions v. New Century Mortgage Corp., 619 F.3d 458 (5th Cir. 2010), which reversed a sanctions award about an arbitration, and FDIC v. Maxxam, Inc., 523 F.3d 566 (5th Cir. 2008), which involved “a proceeding that was not before the district court and did not challenge [its] authority.” In re Deepwater Horizon, No. 15-30265 (June 2, 2016).