Context. Young massive stars in the halo are assumed to be runaway stars from the Galactic disk. Possible ejection scenarios are binary supernova ejections (BSE) or dynamical ejections from star clusters (DE). Hypervelocity stars (HVSs) are extreme runaway stars that are potentially unbound from the Galaxy. Powerful acceleration mechanisms such as the tidal disruption of a binary system by a supermassive black hole (SMBH) are required to produce them. Therefore, HVSs are believed to originate in the Galactic center (GC), the only place known to host an SMBH. Aims. The second Gaia data release (DR2) offers the opportunity of studying HVSs in an unprecedented manner. We revisit some of the most interesting high-velocity stars, that is, 15 stars (11 candidate HVSs and 4 radial velocity outliers) for which proper motions with the Hubble Space Telescope. were obtained in the pre-Gaia era, to unravel their origin. Methods. By carrying out kinematic analyses based on revised spectrophotometric distances and proper motions from Gaia DR2, kinematic properties were obtained that help constrain the spatial origins of these stars. Results. Stars that were previously considered (un)bound remain (un)bound in Galactic potentials favored by Gaia DR2 astrometry. For nine stars (five candidate HVSs plus all four radial velocity outliers), the GC can be ruled out as spatial origin at least at 2σ confidence level, suggesting that a large portion of the known HVSs are disk runaway stars launched close to or beyond Galactic escape velocities. The fastest star in the sample, HVS 3, is confirmed to originate in the Large Magellanic Cloud. Conclusions. Because the ejection velocities of five of our non-GC stars are close to or above the upper limits predicted for BSE and DE, another powerful dynamical ejection mechanism (e.g., involving massive perturbers such as intermediate-mass black holes) is likely to operate in addition to the three classical scenarios mentioned above.