Interesting point, John; I too know people who have good voices and have not had formal vocal training. However, going back to Paula's post I am guessing that some of her reception class pupils may turn out to have great voices as adults but would say they had never had any vocal training, because the seemingly fun singing games experienced at school probably are not recalled as having been "vocal training". So I would be inclined to scrutinise the claims of any brilliant singer who says they have had no vocal inputs; the inputs/stimuli may not have been recognised as pertinent to singing skills.

I fully accept that some folks get a head start in terms of what Mother Nature hands them; perhaps in attentive listening, accuracy of recall, vocal apparatus and reproduction of sounds etc. My position is that no talent is simply a case of either nature or nuture; it is always a complex interaction of both (neuroscience is opening whole worlds of understanding in this arena) and for each person the balance of that equation is different. So for any person who asks the question that is the title of this thread, the answer will be a different one and may be an unknowable one without some formal analysis.