We re-examine evidence that the Galactic Center Excess (GCE) originates primarily from point sources (PSs). We show that in our region of interest, non-Poissonian template fitting (NPTF) evidence for GCE PSs is an artifact of unmodeled north-south asymmetry of the GCE. This asymmetry is strongly favored by the fit (although it is unclear if this is physical), and when it is allowed, the preference for PSs becomes insignificant. We reproduce this behavior in simulations, including detailed properties of the spurious PS population. We conclude that NTPF evidence for GCE PSs is highly susceptible to certain systematic errors, and should not at present be taken to robustly disfavor a dominantly smooth GCE.