Um, the author seems a little confused. Absence of evidence ... is evidence? Excuse me, but no. Absence of evidence means you have insufficient evidence to draw a conclusion which would be favored by the evidence.
Riffing on the black swan example: if someone claims that black swans existed, and someone else is skeptical, the onus is on the pro-black-swan side to provide evidence. The onus is not on the black swan skeptic to believe them.
However, there is a difference between the skeptic saying "I am unconvinced" and "therefore black swans (probably) do not exist." Failing to agree is not the same as strongly disagreeing.