When you’re looking for a thread and no results are found, you’ll be offered to search using Google. I think that you should be able to change the search engine (in preferences) from Google to one of the other three “major” search engines.
Maybe administrators could have the option to disallow users from changing the search engine? Maybe administrators could change the default search engine to Bing, Yahoo, or DuckDuckGo (or back to Google if they ever feel like it)?
Feel free to ask for more information. Questions and constructive criticism are welcome.