Standard models of astrophysical accretion disks--the so-called α-models--assume an ad hoc viscous stress which scales locally as the total pressure: t_r{PHI}_ = αp. In this paper, we show that if turbulent magnetic Maxwell stresses are the source of this viscosity in quasi-stellar object accretion disk models, then the stress cannot follow the assumed α-law in the radiation pressure dominated inner region of the disk. The argument is one of internal self-consistency. First, four model accretion disks which bound the reasonably expected ranges of viscous stress scalings and vertical structures are constructed. Magnetic flux tubes of various initial field strengths are then placed within these models, and their buoyancy is modeled numerically. In disks using the radiation pressure stress law scaling, low opacities allow rapid heat flow into the flux tubes; the tubes are extremely buoyant, and magnetic fields strong enough to provide the required stress cannot be retained. If an alternative gas pressure scaling for the stress is assumed, then the disks are optically thick; flux tubes have correspondingly lower buoyancy, and magnetic fields strong enough to provide the stress can be retained for dynamically significant time periods.