It isn't about capability, it's about € the ESA can't afford to put up Galileo, l suspect that putting up a global navigation system around Mars would be a bit cost prohibitive for this application.
Part of the problem with deploying a GNS is that you need ground uplink station for reference correction (inertial clock correction and fault detection isn't generally sufficient for good long term accuracy). At least they might have less of a problem with ionospheric propagation delay (Mars still has a single layer of ionosphere, though, and since Mars doesn't have much of a magnetic field, it's subject to lots of solar wind effects, so very little is known about correcting for it).
No worries, though, I doubt the ESA isn't thinking about a Martian GNS for this, it's just a research project which happened to use GPS for coarse location. The real technology uses a vision-based navigation supplemented by a laser range-finder and barometer.