The nice thing about "Big Data" is that nobody is forcing you to leave any information about you or your loved ones. Everything you do is voluntairy. Now, as long all sides of the contract (e.g Facebook) holds the terms that are stated in the contract I see no problem, if they donæt then it is a problem but it is not related to Big Data, it is related to morality of humans.
I feel like "Big Data" has become a big buzz word that many people are afraid of. Big Data is in reality a big statistical survey that may be used for both good and evil. What you described, company A giving your credentials to company B has nothing to do with Big Data. Big Data consists of calculating and analysing terabytes and petabates of data. And yes, even you can do it on usual COSTs. Industry standard software is open source and prette easy to use.
RE: "Big data" is not your friend. While having my identity verified for a new credit card, I learned that the cc company requested my identity from my cell phone company.