The proton drip-line nucleus Ne-17 is investigated experimentally in order to determine its two-proton halo character. A fully exclusive measurement of the Ne-17(p, 2p)F-16* -> O-15+p quasi-free one-proton knockout reaction has been performed at GSI at around 500MeV/nucleon beam energy. All particles resulting from the scattering process have been detected. The relevant reconstructed quantities are the angles of the two protons scattered in quasi-elastic kinematics, the decay of F-16 into O-15 (including gamma decays from excited states) and a proton, as well as the O-15+p relative-energy spectrum and the F-16 momentum distributions. The latter two quantities allow an independent and consistent determination of the fractions of l = 0 and l = 2 motion of the valence protons in Ne-17. With a resulting relatively small l = 0 component of only around 35(3)%, it is concluded that Ne-17 exhibits a rather modest halo character only. The quantitative agreement of the two values deduced from the energy spectrum and the momentum distributions supports the theoretical treatment of the calculation of momentum distributions after quasi-free knockout reactions at high energies by taking into account distortions based on the Glauber theory. Moreover, the experimental data allow the separation of valence-proton knockout and knockout from the O-15 core. The latter process contributes with 11.8(3.1) mb around 40% to the total proton-knockout cross section of 30.3(2.3) mb, which explains previously reported contradicting conclusions derived from inclusive cross sections. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).