MonoTouch does not compile to Objective-C. It compiles to native code, just like Objective-C, very much like Mono, CLR, or JVM do on other platforms. The real difference is running the compiler ahead of time, versus JIT. That, and disabling some functions that Apple deems bad, like keeping the ability to modify or emit code on-the-fly.

In the case of MonoTouch, you do get the infrastructure; they have the runtime ported over, and other libraries get compiled in as needed. So, in Mono's case, it IS "running .NET on iOS".

I see no intrinsic reason this could not be done for Java, although I don't know what this specific implementation is doing.