Can you give some examples?. (genuinely curious btw).
I think the wells fargo banking app on the phone is not native. The At&t one doesn't feel like it. Usually there's something different about the controls and interactions that make it not feel native. Sometimes there's a dead giveaway like being able to double tap and accidentally zoom in just like in mobile Safari.
And the spacebar will 80% of the time page down rather than pause the music, something which sounds minor but which makes the user experience 50% more annoying for me. Do most people even use spacebar to page down in normal webpages!?