I think a more simpler solution is to simply ask the devs of the browsers that you use. I don't see why they wouldn't be honest with you considering in most cases the apps are free. If you have opted out of collecting data with Google then it shouldn't transmit anything. However, if the data collection is so deep in the programming of the OS then there isn't anyway to prevent it aside from a possible third party app to block it. Root users of Android (like myself) can get programs to simply block ads and so forth so I imagine someone has developed a program like that. You can also email or contact in some manner Google themselves. They may have a more precise answer. Whether or not they are telling the truth is entirely up to you. If after you have exhausted all possible investigations into preventing data mining there is no possible way to prevent it, well....you're probably SOL and JWF.
Bear in mind, Google's claim to fame is targeted advertising and their search engine. I highly doubt Google themselves will do anything malicious to you or any personal data outside of targeted advertising. Indeed as it has already been mentioned, some of the third party apps are a much greater danger than the core OS.
This is of course the trade off to using Android. I can honestly say that outside of the ads, there has never been any instance of these things you mention. The health care thing could have been possible (before the Obama health care reform), but doubtful. Any of these things that were mentioned already happen now. People have been fired for posting things on Facebook (my current job says that I can't talk bad about my job on Facebook or risk losing employment), health care companies have people who actively search (and find without the use of search engines) for pre-existing conditions and the like.
Your best solution is to talk to the devs. There's always a method to contact them in the Android market where you install the app. If you want some probable first hand experience, I suggest XDA forums in the Android section where active programmers are. They will have the most intimate knowledge of Android and may even have a custom ROM that might have no data mining. Hopefully, this, while not completely answering your question, will at least point you in the right direction to finding the answers you seek.
