That was a major concern of mine. You can set the Research mode to "Off" by default and check URLs on a case-by-case basis and still do custom searches. Admittedly, it takes some of the serendipity out of it, but it addresses your concern.
I considered (and was planning on) adding a "block URL" feature - but the issue of how to store those sensitive URLs (to block) came up. Because localStorage and sync storage in Chrome is not sandboxed or encrypted, the blocked list would be "in the open" to other extensions. Yes, you could hash the urls you'd hope to block, but then there would be no way to read that list back to the user at a later point in time, and slight mismatches in URL schemes would lead to an imperfect system. So simply toggling Research Mode and researching pages of interest is the best option, IMO.
I don't cache any personal info in localStorage or sync storage (which at least Chrome does not encrypt :< ). The api results are stored in a local variable within the scope of the extension. And the "history" is a hashed and padded blob.
This is also why I released it for both Chrome and FF, since some people assign different use cases to different browsers. The code is also public/open-source.