The basic premise seems to be that the Arabs and the Turks didn't know anything about Western culture, and weren't interested in learning anything about infidels. They borrowed the weapons after they got their asses handed to them, and then after they still had their arses kicked, they borrowed the Western organization and bureaucracies that came with it. Then they still got their arses kicked, because they didn't do any science themselves and didn't and couldn't keep up with the West (again, because they didn't know enough about Western culture.)
Not only that, the very idea of knowing Western culture was and is inimical to the very idea of Islam (as practiced, anyway). When these guys are by definition unbelievers and inferior, it's a real kick in the teeth to have to have to borrow anything from them. The biggest problem was not that they couldn't borrow the technology or the ideas... it's that the people they sent out to the West to steal the forbidden fruit would come back with ideas that were... not Islamic. In fact, the infected diplomats and emigrants were more of a problem than the West -- the West was out there, but it was a thing apart, and defined as 'enemy'. But any people coming back from the West would be talking heresy from top to bottom, from Women's rights, to the lack of slavery, to the separation of Church and State.