The hypethetical scenario is that the person doesn't fit the definition of atheism, but chooses to use that word to describe themself, knowing that the theist will be shocked that someone would hold such an irrational position, then the self proclaimed athiest reveals that they hold a position that is different from the literal definition of the word atheism.
People are different. Any term used to describe more than 100 people needs to be broard, because that many people hardly ever totally agree on anything.
An atheist is simply someone who does not believe in whatever god is currently being discussed. Of course there are varying degrees to it, strong- weak- positive- ..of course people want to describe their positions more accurately. It's the same thing with any word that describes a large amount of people, simply because people are different.
It's the same with Catholic. Strict Catholic.. Practicing Catholic.. Non-Practicing Catholic.. People are different. When so many people get labelled with the same term qualifiers and identifiers are always invented to add distinction. But only used when such specification is desired.
My name is Geoffrey Robert Rastas. When I meet someone I say "Hi, my name is Geoff". This is not lying, this is not being deceitful or disengenuous. This is being sufficiently specific. Not only will most people not care to hear my full name, but it's hardly worth the breath to draw any idle conversation out to any longer length. If someone is interested to learn more about my personal indentification, they are free to ask.
I doubt that any one person can totally sum up their full beliefs in a single identifying word which can be used to equally and validly describe a handful of others, let alone millions.
Yes, many people will call themselves atheists. You now know they do not believe in god. If you'd like a more specific answer.. you're just going to have to ask.