The searches are not the only things that point to a possibility of a guilty verdict. And he did show that original they were mistaken when they thought he made the searches himself. So I am not sure it was an outright lie on his part.
Staley discussed just this issue in her Jan 2016 ruling denying the DT's motion to suppress electronic evidence, ALL of it predicated on LE's word RH had conducted those searches.
It may interest you to know she specifically cited GA code about whether or not LIES by LE on search warrant affadavits invalidated the legality of the warrants obtained.
Astonishingly, at least IMO, her ruling was that it's legally permissable for LE to lie in order to obtain search warrants, as long as the magistrate reviewing the affadavits believes there is, overall, probable cause to justify the warrants. Of course, the only info available to the magistrate is that being provided by LE.
See how that works?