Shoot... I answered this before but I guess the computer ate my answer.
First, I completely agree with the second answer in that it emphasizes that European civilization started long before Islam arose. For that reason, you can't say Muslims started European civilization.
Second, it is not clear to me that Europe (if there really is such a thing as all European opinion) denies that Muslims kept the learning of the Greeks and Romans alive during the Dark Ages. Because they did this, Europeans were able to relearn what previous Europeans had known.
Third, I think one reason you wouldn't say Muslims are behind European civilization is the fact that European civilization and Muslim civilization (again, to the extent that these are monolithic things) have diverged so much in the years since the Muslims were expelled from Spain in 1492. Therefore, European culture is so different now from most Islamic cultures that the connection is no longer very obvious.
There are several reasons why Muslims were not the creators of science.
1. Muslims came onto the scene much later than many great technological advances, which were discoverd by the Greeks.
2. The Greek made great strides in science, medicine, and philosophy before Islam. In fact, over 1000 years before Islam. Hippocrates and Aristotle are great examples.
3. The Islamic world got a lot of scientific knowledge from the Hellenistic world that made great strides in science. Archimedes was an Hellenistic figure. They were able to do this through conquest.
4. Some of the things that they learned was reshared with Europe, but they got it from the Greeks.
I suspect that anyone who knows anything about the early history of science would not deny that Muslim peoples were generally far advanced in comparison to their northern European neighbors, especially in the areas of mathematics and human anatomy. However, this statement shouldn't be taken to mean that Muslims were the creators of science. David C. Lindberg (see the link below) presents a compelling argument that
Islamic science [can be seen] as the end product of the diffusion and assimilation of Greek science in parts of North Africa and Asia. In turn, Islamic science served as a means of transmission of Greek science back to Western Europe.
In other words, the Greeks gave knowledge to the Muslims, and the Muslims gave knowledge to Western Europe. On a personal note, I should add that I like this model; the West is indebted to the Middle East, absolutely, but that fact doesn't make the Middle East the center of all knowledge, either. Human communities add to and pass along information. It's what we do well.