Can a lack of evidence be considered proof?

[Minimalist]

Absence is evidence of absence.

The absence of evidence for a particular claim is evidence that the claim is false.  The conclusion can be overturned if subsequently evidence of the claim is uncovered.

Kenneth Kitchen's mantra is frequently misapplied by jesus freaks when, for example, archaeologists state that there is no evidence of a major city during the 10th century in what is now known as "Jerusalem."  The nut jobs insist that we have to keep looking for their version of Shangri-La but what archaeology has found at 10th century levels is evidence of a shitty little one-horse village.

Thus what they are claiming is that there is absence of their evidence which is a whole other kettle of fish.