Recent experimental observations using tracer visualization techniques have suggested that even for low Reynolds number flows, the steady vortex breakdown bubble in a torsionally driven cylinder is not axisymmetric and has an inflow/outflow asymmetry at its tail. These results seem to suggest that this type of vortex breakdown is closer in structure to that observed in the open vortex tube than previously thought. In this paper we examine numerically the effect of imperfections in the rig geometry, in particular quantifying the effect of a very slight misalignment between the axis of rotation of the end plate and the cylinder axis. It is shown that even slight misalignments, which are unlikely to be measurable experimentally, can produce the main details of non-axisymmetric open breakdown bubbles that have been observed in many experiments. This provides a resolution to the mismatch between the axisymmetric and closed bubble predictions of three-dimensional numerical simulations and stability analysis, and the observations of open bubbles often apparent even in carefully controlled experiments.