Cocoa Touch has everything built in to pull this off. I'm working on an app right where the ui is "completely custom". I say it like that because I'm using all the default Cocoa Touch stuff, just "skinned" as you will.
Just because it's looks good doesn't mean it's an HTML5/JS app.
Get out of the mindset that Objective-C and Cocoa can't do this kind of stuff. With ObjC you can do pretty much anything your mind can imagine (within the hardware limits of the iPhone or iPad).
If you're curious about how to implement the stuff look up UIAppearance, and google stuff like "how to implement a custom UITabBar"