I'm a heavily accented non-American, non-British (though I can claim English is my native language since it's been my language of instruction since Kindergarten).
Google's voice recognition system, and of late, Siri both work fine for me. Sync, iPhone 'voice control', etc. are next to useless. In certain cases, I've tried to adapt. For example, my immediate family, rather than have their names or what I call them in my other native language, I've named them using common English words. So I can just say "Call Dad", and the speech recognition system works.
When I say that OEMs and auto-makers should work on improving voice recognition systems, I mean the entire processing system: sound acquisition, signal conditioning, and machine-learning based speech recognition.