I've never heard of a single atheist in history try to make that argument.

Here is one.

You are right that atheists rarely use the word "impossible", just like I don't say it is impossible I am a brain in a jar only imagining I am writing this, or that 2+2=7. It's just that I consider it so unlikely I don't consider it a real possibility. There are plenty of atheists, including on reddit, who won't use the word "impossible", but nonetheless have made up their minds and don't seriously consider the possibility anymore that there might be a God. Here is another atheist stopping short of saying "impossible", but still making it clear that his mind is made up.

However, since I did use the word "impossible", you are correct. Not many atheists are atheists in the sense I used above. Then most people who call themselves atheists are really agnostics, maybe even Mr. Jillette.

As for the authenticity of my definitions, this is the definition of "atheist" from what was once the standard dictionary of common usage and this is the definition of agnostic. Perhaps you are too young to remember, but before what you called " the four-types 'a/gnostic a/theist' method of definition" started to become popular not too long ago, these are what pretty much everybody meant by these words. Maybe I should just get used to the fact that these words are often now used differently than when I first learned them. But in my comments above, those are the definitions I had in mind.