> they mean that people hold atheism in a religious way
And how many atheists actually do that? I think what GP meant was more about people who just somehow can't imagine being religionless (and "the more advanced cases" paragraph hints it very strongly), not about people who point out that some atheists hold their atheism religiously.
Anyway, your points seem wrong to me. After Wikipedia - "Atheism, in the broadest sense, is an absence of belief in the existence of deities." Absence of belief does not answer any questions by itself, and considering its provability doesn't even make sense at all. What you said may make sense for the less broad definition ("In an even narrower sense, atheism is specifically the position that there are no deities"), but that's not what "atheism" usually means without any further qualifiers.
For me, atheism is a natural consequence of realizing that I have no more reason to believe in existence of any particular god than any other fictitious being - and even if I did assume that a god exists, I would still have a hard time choosing which god is it, as there are many contesters and none of them has any obvious advantage when it comes to believability. There are many believable reasons why religions exist, but none of them implies that any religion is actually true (to the contrary, the history of some well-known religions seems to make it pretty clear that they were products of human culture).