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The assumption that black hole accretion disks possess an untorqued inner boundary, the so-called zero-torque boundary condition, has been employed by models of black hole disks for many years. However, recent theoretical and observational work suggests that magnetic forces may appreciably torque the inner disk. This raises the question of the effect that a time-changing magnetic torque may have on the evolution of such a disk. In particular, we explore the suggestion that the" deep minimum state" of the Seyfert galaxy MCG-6-30-15 can be identified as a sporadic inner disk torquing event. This suggestion is motivated by detailed analyses of changes in the profile of the broad fluorescence iron line in XMM-Newton spectra. We find that the response of such a disk to a torquing event has two phases: an initial damming of the accretion flow together with a partial draining of the disk interior to the torque location …