I'm technical, and I couldn't care less about search security/privacy.
The page screams out to me "solving a problem that doesn't exist". Why do I care that Amazon knows that I searched google for "shoes"??? Surely that's useful info to pass on to Amazon. In what instance would I care? I can't think of any...
The way a startup will win against Google is by doing what Google did 10 years ago. Give users better, clearer, faster, more streamlined results.
Whilst Google is chasing silliness like 'real time update results' - WTF do I care what people are saying on twitter? - a startup can stick to what people actually want - clean search results.
Pandering to an extremely small niche of privacy freakouts, I don't think is a scalable strategy.
(just my 2c)