The implication here is that Greek culture had to be brought to the West. Let's say it plain: Greek culture IS the West.
The Roman Empire in the East did not fall in the Dark Ages. The Empire based at Constantinople -- and which used the Greek language, remained powerful for almost 1000 years after Rome fell. It was rich, cultured, and militarily dominant for much of this time.
Monasteries of Europe held on to much ancient culture, and the Byzantine Empire based at Constantinople held on to much more. Yes, one can say that some culture was held in the Middle East, and the Arabs did have some access to things which they preserved -- but their role is not nearly as significant as some seek to claim.
Note also that Muslim conquerors such as Tamerlane destroyed much culture in the Middle Ages, and left mountains of skulls in the Middle East and in India. Tamerlane was not an anomaly. He was reasonably standard for Muslim conquerors -- the more gentle, cultured Muslims were the exceptions to the rule.
In short -- if one wants to say that Muslims in the Middle Ages were better than Muslims today, that may be true -- but the Muslims of the Middle Ages were no prizes either.
Although Tamerlane used Islamic ideas and forms to promote his program of conquest, I have the distinct impression that his primary goal was restoration of the Mongol empire built by Genghis Kahn, not the promotion of the Caliphate. The link below describes 3 great conquerors in detail. Tamerlane is the most recent, and the information provided after you click “more” is quite detailed and complex. He was not shy about destroying a number of important Islamic cities.
http://asianhistory.about.com/od/profilesofasianleaders/p/TimurProf.htm