How have courts interpreted the phrase "proof satisfactory to the decision-maker" in the context of a disability benefits application?

[T]he phrase "proof satisfactory to[the decision-maker]" is an inadequate way to convey the idea that a plan administrator has discretion. Every plan that is administered requires submission of proof that will "satisfy" the administrator. . . . [T]he administrator's burden to demonstrate insulation from de novo review requires either language stating that the award of benefits is within the discretion of the plan administrator or language that is plainly the functional equivalent of such wording. . . . [C]ourts should require clear language and decline to search in semantic swamps for arguable grants of discretion.

Kinstler v. First Reliance Standard Life Ins. Co., 181 F.3d 243, 252 (2d Cir.1999).