How is Xamarin not native? It's compiled right, not some web view hybrid?
Yes, Xamarin produces a compiled executable, as you would get in Swift or Objective-C. It is not a web view hybrid.
I work for Microsoft
By Native iOS you mean not written in Objective-C/Swift using Cocoa Touch
Xamarin uses Cocoa Touch. It gets compiled to the same thing as something written in Swift. So definitely iOS Native.
Not really the same thing...
I believe the cococa touch API is exposed like for like in xamarin.
You are correct. They actually have a tool that scans the Cocoa libraries and generates API bindings for Xamarin to use. Source: Miguel De Icaza on the .NET Rocks podcast.