I think you are mistaking atheism with strong-atheism.
Nontheism is not specifically about gods & was also not in the options made available by the maker of the poll.
Very few atheists are strong-atheists as you stated, it's illogical because it would require proof (which there is none either way - but I'm not exactly sure how one would find proof that something does not exist).
I'd like for somebody to find proof that Goblins don't exist.
A bit from wiki (I'm not a walking dictionary so sue me).
Explicit atheism is defined as "the absence of theistic belief due to a conscious rejection of it".
Explicit atheists have considered the idea of deities and have rejected belief that any exist. (in our case due to no evidence).
Implicit atheists thus either have not given the idea of deities much consideration, or, though they do not believe, have not rejected belief.
Only strong-atheism accounts for the requirement of a belief (as a position is held which requires defending).
Weak/Strong and Implicit/Explicit are not the same categories, although admittedly it probably does help that the new atheist movement keeps trying to redefine the various terms on a regular basis in an attempt to both expand the base of atheists and try to reduce the criticism of the logical inconsistency of attacking faith based positions.
Traditionally, The positions are defined as follows:
Weak (or Negative) Atheism - Disbelieves the existence of deities, commonly due to absence of acceptable evidence. Open to change if evidence presents.
Strong (or Positive) Atheism - denies the existence of deities, not open to change.
Explicit atheism - Makes a conscious choice to disbelieve or deny the existence of deities.
Implicit atheism - lacks an explicit believe in the existence of a deity or deities.
In generally accepted (eg accepted by more than just the new atheist fringe), atheism covers explicit atheism in both strong and weak varieties, but not implicit atheism. (The terms explicit and implicit were defined by George H. Smith in his 1979 publication 'Atheism, the case against God'). There's a variety of reasons why this is the case, but most fundamentally, it's rather hard to discuss a position in a meaningful manner that people don't self identify as a group.
The issue is further compounded by the multiple possible definitions of the use 'Belief' when in a religious context. I don't, for example, 'believe in' the Christian god, but my lack of theological belief has no bearing on the question whether I think the christian god exists or not, which I consider irrelevant. In this respect, although I lack an explicit belief in the christian god, I cannot be considered atheist towards it.
Perhaps it would be better, though, if we could agree on a common set of terms and debate the points rather than the language, because otherwise we aren't likely to progress.
On the evidence point around Goblins, the scientific method does provide a means to achieve this, provided we can sufficiently define the hypothesis and evidence in such a way that you can bypass the problems of induction, and equate an absence of evidence to be evidence of absence.