Recent thorough experimental activity aiming to generate high harmonics in the SF6 molecules requires the knowledge of, on one hand, accurate valence-shell photoionization cross sections and phases, from a threshold up to a few tens of eV, where resonances are likely to appear, and, on the other hand, the effect of the nuclear vibrational dynamics on the process. In this work, we have experimentally determined and theoretically evaluated vibrationally resolved photoionization cross sections of SF6 up to 80 eV photon energies, with an emphasis on the (ET1u)-T-2 channel, for which vibrational progressions are fully resolved in the experiment. Our results reveal the presence of shape resonances due to excitation to SF6 virtual states lying just above the ionization threshold, in agreement with previous synchrotron radiation work and theoretical calculations. More interestingly, our calculations also disclose resonance features at photoelectron energies as high as 40-50 eV, which are due to the transient confinement of the ejected electron in the octahedral cage formed by the peripheral F atoms. In the vicinity of all resonances, including those due to confinement, the calculated ionization phases experience an excursion of about pi or pi/2 and significantly depend on the final vibrational state of the remaining cation. Both effects should be taken into account to correctly interpret ongoing high-harmonic generation work in SF6. A similar behavior is expected for other symmetric molecules containing a central atom, such as BF3, CF4, and the like.