We revisit theoretical and observational constraints on geometrically-thin disk accretion in Sagittarius A* (Sgr A*). We show that the combined effects of mass outflows and electron energization in the hot part of the accretion flow can deflate the inflowing gas from a geometrically-thick structure. This allows the gas to cool and even thermalize on an inflow timescale. As a result, a compact, relatively cool disk may form at small radii. We show that magnetic coupling between the relativistic disk and a steady-state jet results in a disk that is less luminous than a standard relativistic disk accreting at the same rate. This relaxes the observational constraints on thin-disk accretion in Sgr A* (and by implication, other Low-Luminosity Active Galactic Nulcei, LLAGN). We find typical cold gas accretion rates of a few * 10-9 Mo yr-1. We also find that the predicted modified disk emission is compatible with existing near-infrared (NIR) observations of Sgr A* in its quiescent state provided that the disk inclination angle is >approx 87^o and that the jet extracts more than 75% of the accretion power.