I'm not quite sure I understand his objections to Xamarin. He says, "It can only output to intermediate Xamarin libraries, not native ones."

On iOS Xamarin does compile down to native code and on Android is compiled to dex format. They are not interpreted on those platforms.

Xamarin can utilize PCL assemblies, so non-ui code could be written once and used multiple places without recompilation. This is actually very handy since those libraries can be built on Windows, where the toolchain is better (IMO VS is better than XS) and the system is more powerful.