The cartoon below shows how the research community sees target specificity of ZFs, CRISPRs, TALENs, etc. The idea is that you get lots of hits on the exact target sequence but the further away you get this falls to some background level - the 'random' hit rate if you wish. To measure this you gene sequence the target site itself and then sites that are off by just a few base pairs and then a few more, etc. In the current state-of-the-art deep sequencing CRISPR study (which I have cited many times here) they found 'hits' dropping below the level of detection for sites only a few base pairs away from the target sequence and so rightly concluded that the background (random) hit rate is negligible. Sangamo has done much the same thing with ZFs.
As best I can tell zinc thinks this curve dips to (near) zero at a few base pairs difference and then jumps back up farther away in places not measured. He has no logical explanation for this and cannot cite any study that shows it but expects us to all believe it because he says so.