Direct experimental investigations of the low-energy electronic structure of the Na2IrO3 iridate insulator are sparse and draw two conflicting pictures. One relies on flat bands and a clear gap, the other involves dispersive states approaching the Fermi level, pointing to surface metallicity. Here, by a combination of angle-resolved photoemission, photoemission electron microscopy, and x-ray absorption, we show that the correct picture is more complex and involves an anomalous band, arising from charge transfer from Na atoms to Ir-derived states. Bulk quasiparticles do exist, but in one of the two possible surface terminations the charge transfer is smaller and they remain elusive.