"Historians generally consider the Dark Ages to have begun in the fifth century, when a series of barbarian peoples invaded the Mediterranean world and destroyed urban civilization."
The Germanic "barbarians" did not destroy Mediterranean civilization. The various Gothic rulers of the Italian peninsula kept the Roman administration and city structure functioning as it had been for centuries.
Credit for the destruction and depopulation of urban areas in the Mediterranean goes to the decades long war of reconquest of the Italian mainland by the forces of the Byzantine Emperor Justinian and his general Belisarius.
The Visigoths, who lacked a tradition of urban government and who were faced with the legal and administrative needs of a large subject population, did indeed adopt and maintain much of the form of Roman government. However, the titanic economic devastation incurred (such as superinflation and Diocletian's edict essentially terminating the free market) by centuries of warfare against the Germanic barbarians had long since doomed the Roman Empire, years before the hordes themselves finally broke through and physically destroyed places like Aquileia, Cologne, and Rome.
That the Germanic barbarians used Roman forms to preside over the civilization they had destroyed is not surprising. To pretend that what they ruled was still Roman civilization, however, is erroneous.