Atheist VS Naturalist - the latter sounds more appealing to me...

[polymath257]

So, in your little scenario, the scientists would NOT say it is impossible for a frog to sing. They would observe it singing and start with that information, proceeding to try to figure out how it is possible.

This is a re-statement of what you said before. I understand what you've been saying.

You are sure that anything that happens is natural. You rule out the supernatural a priori. 

You are very committed to this metaphysical view. You may well be right.

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What you seem to miss is that it follows from *your* definition of natural.
 
You *defined* the 'nature' of something to be 'what it is or does'. So, *whatever* it does is, by *your* definition, natural.

If you *don't* mean that as your definition, then be more clear about your definition.