No, I am talking about when one can be "intellectually honest" saying that they know. And your two very differing standards based on who is saying it.
When I said that an “intellectually honest” atheist would probably have to identify with agnosticism, I was following another poster’s idea, namely, that there’s not really a difference between atheism and agnostic atheism. The reason for that comment didn’t get fleshed out, but I’m guessing it’s because claiming that you’re a gnostic atheist is an extraordinarily strong statement. While theists can have different notions of God and various ways at arriving at his existence, a true gnostic atheist is saying that they’re all false. God does not/ cannot exist. Well, good luck trying to produce a direct proof towards that end.
Regarding the “proving the negative” issue, I think that’s only a problem if you assume the starting point is gnostic atheism. So, if you’re presented with a proof of God’s existence and you refute it, then you move back into the gnostic atheist camp.
However, that’s not how it works in practice. For example, most of my atheist friends’ starting position is that they have no knowledge of God, one way or the other. So, uncertainty is baked into the cake and they assume God doesn’t exist until proven to the contrary. But they don’t really know for sure. Therefore, they are agnostic even if they don’t understand it. Then, their degrees of belief move along the agnosticism/ skepticism spectrum as they experience life and gather evidence.
My point is that I would assume for them to move into the full-on gnostic atheist camp they would need a formal direct proof or concrete evidence that God doesn’t exist. Otherwise, I don’t know how you move from agnosticism to stating that you know with certainty that something like atheism is true.
Proving God exists would support you "knowing", but that isn't the point. The point is that if you are claiming that you can know based on belief at the same time others cannot, then you are exerting a double standard. A disconnect. Or a blind spot.
There are a lot of folks who think that God’s existence has been proven. And yes, with rigor. Indeed, this is exactly what Thomas Aquinas thought and ditto with other great philosophers and theologians. These people claim that they have a direct proof (or set of proofs) that move them into the fully gnostic theism category. Moreover, there are others who claim divine revelation for one reason or another.
As for what it means to truly know something vs just believing in it, I feel like you’re moving the goalposts to an argument over epistemology/ philosophy of mind. That, or you’re trying to tell me to prove that God exists or admit that I’m an agnostic theist. Or worse, you’re using it as a way of dismissing philosophers like Aristotle and Aquinas out of hand.