AFAIK, the OS-specific Qt themes don't wrap the native widgets, it reimplements them. They are rather thorough though, making sure their OS-specific theme matches the look and behavior of the native OS, which makes it one of the best framework to do something that feels close to native.

No, it's just the most accurate re-implementation that I know of at least for Windows.

You can sometimes tell the difference because the QT emulated widget can do things that the native widget can't.