The question in play is whether one can make a general statement about the impossibility of proving a negative. The answer to that claim is "no." (Because one can produce examples where a negative statement can in fact be proved, as in math, the general claim is demonstrably untrue.)
This is not to say that one can always prove a negative -- I'm perfectly happy to accept that there are cases where one cannot do so. The problem comes when one tries to make a general claim.
That being the case, then any particular statement must be addressed on its own terms. The question of proving the non-existence of God ... I have no idea what the form of such a proof might take. (Actually, I rather doubt it is possible to find one, having decided based on my own experience and obvservation that He does exist.)