Electronic structure of LaAlO3/SrTiO3 (LAO/STO) samples, grown at low oxygen pressure and post-annealed ex situ, was investigated by soft-x-ray ARPES focussing on the Fermi momentum (kF) of the mobile electron system (MES). X-ray irradiation of these samples at temperatures below 100 K creates oxygen vacancies (VOs) injecting Ti t2g-electrons into the MES. At this temperature the oxygen out-diffusion is suppressed, and the VOs should appear mostly in the top STO layer. The x-ray generated MES demonstrates, however, a pronounced three-dimensional (3D) behavior as evidenced by variations of its experimental kF over different Brillouin zones. Identical to bare STO, this behavior indicates an unexpectedly large extension of the x-ray generated MES into the STO depth. The intrinsic MES in the standard LAO/STO samples annealed in situ, in contrast, demonstrates purely two-dimensional (2D) behaviour. The relevance of our ARPES data analysis is supported by model calculations to compare the intensity vs gradient methods of the kF determination as a function of the energy resolution ratio to the bandwidth. Based on self-interaction-corrected DFT calculations of the MES induced by VOs at the interface and in STO bulk, we discuss possible scenarios of the puzzling 3D-ity. It may involve either a dense ladder of quantum-well states formed in a long-range interfacial potential or, more likely, x-ray-induced bulk metallicity in STO accessed in the ARPES experiment through a short-range interfacial barrier. The mechanism of this metallicity may involve remnant VOs and photoconductivity-induced metallic states in the STO bulk, and even more exotic mechanisms such as x-ray induced formation of Frenkel pairs.