Earlier quoted context omitted.
They are not OS-native, but they use OS theming information.
Right. Browsers can't use the OS control implementations, because the demands of DOM/CSS simply can't be handled by those native implementations. But Firefox is trying to emulate the look and feel of the OS controls, using native theme drawing APIs when possible. It is very hard to get 100% right, which is why no browser does.
This is not correct. In instances where CSS doesn't affect the styling of the control, the browser can use native controls. As far as I know, every browser _except_ Firefox does this. For example, elements in Chrome and Safari are native elements (albeit Win32 versions in the former on Windows).