Nope, thats not what i said. I did acknowledge that religion is a factor, it is one amongst many. You however, want to make it the only one, for whatever purposes.
Here are the factors that usually affect a country's condition:
1) The relation between religion and government. The more defined, organized, realizing justice for all those under it, not forcing it on others etc... the better a country's conditions become.
2) Education.
3) Political circumstances and history (which should speak for itself, i hope).
4) Culture and religion in general.
5) Social issues.
6) Financial position.
All of these factors contribute to whether or not a country is doing good. Muslim societies share many, and in some cases all the same problems regarding those points.
Now, regarding your other claim, that non-religious societies, that can simply be addressed by the fact that all sorts of different societies had ups and downs, sometimes while being religious and some times while not. In other words, Muslim societies were at one point at the peak of power and accomplishments, now they're not doing too great. And actually, just an aside, they're now less religious than they were at their peak.
Other countries, which were more inclined to being non-religious, at some points were horrible examples of corruption and fascism, while at other points, are doing good for themselves, such as many examples today. So, in a nut shell, you can't claim that Islam is responsible for the circumstances of these countries, any more than non-religiousness is responsible for the corruption of the likes of Russia in the times of Stalin, or China today.