Unfortunately - on platforms where Qt isn't the native UI already - Qt just emulates (draws) the native UI, it doesn't actually use the native UI controls.
On Windows, Qt does a very good job of emulating the native UI. But then again I'd argue that Windows has few truly native UIs. You always notice small differences in how controls behave between different apps. I guess all the different versions of MFC, WPF, VCL, WinForms and whatever implement controls slightly differently from what the Win32 API offers and even between different versions of itself. But users are used to these inconsistencies, so no big deal.
On OS X, the situation is unfortunately a lot worse, probably because Cocoa is so different from everything else that it's hard to emulate properly using primitives from other toolkits. For example you can notice that Qt draws the focus border around buttons differently than Cocoa does. The biggest difference being that Qt buttons are focusable but Cocoa buttons are not. Toolbars also look different: in Cocoa they blend in with the window title bar. Qt doesn't do this - the toolbars look very much Windows-like. The border spacings and alignment are also off. Developers often don't take time to align and space all the controls properly to give them a Cocoa look.