The gas from which stars form is magnetized, and strong magnetic fields can efficiently transport angular momentum. Most theoretical models of this phenomenon find that it should prevent formation of large (>100 AU), rotationally-supported disks around most protostars, even when non-ideal magnetohydrodynamic (MHD) effects that allow the field and gas to decouple are taken into account. Using recent observations of magnetic field strengths and orientations in protostellar cores, we show that this conclusion is incorrect. The distribution of magnetic field strengths is very broad, and alignments between fields and angular momentum vectors within protostellar cores are essentially random. By combining the field strength and misalignment data with MHD simulations showing that disk formation is expected for both weak and misaligned fields, we show that these observations imply that we should expect disk fractions of ~10 - 50% even when protostars are still deeply embedded in their parent cores, and even if the gas is governed by ideal MHD.