They do, and they used a mobile atomic clock to compare the times. The problem is that both locations are in different, accelerated frames of reference, so reasoning about time in those frames of reference can become non-trivial.

Apparently they didn't use a mobile atomic clock but a mobile gps clock to compare the times: http://operaweb.lngs.infn.it/Opera/publicnotes/note134.pdf So it appears they synchronized both timing sources with an orbiting clock, and the critique from this dutch guy seemingly stands.