Diana seems the kind of woman who wouldn't trawl the Internet very much, just mostly sticking to news sites and non-profits because, let's be honest, if she ever went onto any log that would mention Japanese tentacles, chances are she'd also come across some kind of smarmy/sexist comments about her. (Wasn't there a JLA episode where she got upset about some TV talking head comparing her outfit to a Vegas showgirls'?) She'd probably get upset, but eventually think those areas of the Internet were too negative and not worth her time and therefore not frequent similar sites.