I believe this is an erroneous misinterpretation of science and it's practice. Part can relate to Occams razor.
Occam is the one that states that given two or more competeing explanations/theories/etc. where all evidence is equal, the simplest explanation is the most rational explanation [given the evidence at hand].
It is only human nature that leads to the erroneous belief that a lack of evidence is disproof of anything. Rational thought, however, does give us Occams razor. The razor is a rational method for dismissing explanations that expound unfounded 'reasons', without bound.
Since I've never heard of a scientific theory that has been or could be proven, I'm a little skeptical of the rest of the quote.