The predicted acceptor impurity nature of carbon in hexagonal GaN grown by molecular-beam epitaxy (MBE) is revisited spectroscopically in the energy range between 1.6 and 3.5 eV. Photoluminescence (PL) spectra from ultra-pure GaN and material doped with carbon at a level of 1·18 cm⁻³ differ significantly in the energy range between 3.0 and 3.3 eV depending on the Ga/N stoichiometry during MBE growth. Acceptor-like features formerly attributed to carbon, beryllium or magnesium incorporation are found for both, undoped and carbon-doped GaN. The intensity of these features depends on the Ga/N stoichiometry during growth. While for Ga-lean surface regions, exhibiting multiple 10 nm deep pits, the observed PL features are found to be less intense compared to Ga-rich surface regions, the situation reverses for carbon-doped material. For all samples, the intensity of the yellow luminescence band around 2.2 eV is weak. The results point at crystal defects and the unintentionally present oxygen as the origin of the spectroscopic features traditionally attributed to carbon in GaN.