Twitter is primarily designed to help you share information with the world. Most of the information you provide us through Twitter is information you are asking us to make public. ... Twitter broadly and instantly disseminates your public information to a wide range of users, customers, and services, including search engines, developers, and publishers that integrate Twitter content into their services, and organizations such as universities, public health agencies, and market research firms that analyze the information for trends and insights. When you share information or content like photos, videos, and links via the Services, you should think carefully about what you are making public.
I could swear an earlier version even pointed out that tweets you delete are not gone, because, by the time you delete it, it's already been permanently archived by a zillion third parties. I can't find anything about that in the current version, though.
I suppose Twitter's in an easier spot here, though. Like they say, Twitter's for talking to the whole world. Whereas, when people use Facebook, they typically use it to communicate with a more intimate circle.
We do have other approaches. That I can obtain your employment contract, take your picture as you walk in and out of buildings and when you visit the beach, figure out your birth day and who you hang out with...
...doesn't mean I'm allowed to or freely share/sell every detail of your life.
We could for example create a license or permit for gathering a type of data. Like: If you are a dating agency you can ask for peoples sex. If you are a head hunter you may gather data on employment history. If you have a taxi service you can ask for peoples address.
We could also adopt a government issued key for things like signing petitions.
Where the data is stored could also be subject to regulation. Its possible to keep access logs with specific justification for each bit of sensitive information accessed.