What the hell? Wasn’t Facebook quite an offender to you the last time over privacy issues? You should be able to opt-out of this in Twitter fairly but according to the recent lawsuit someone had filed, it appeared that the secret offense Facebook had came from Twitter in eavesdropping on Direct Messages by collecting data for advertisements during Twitter servers with the use of shortened links. Certain kinds of shortened links would show me a blank page like things had no response whatsoever on purpose but illegal eavesdropping from a company on their users is what spreads stupidity all over.
You should keep in your bloody mind that not a single tweet is private when everything is shown to both followers and non-followers. That surely includes direct messages as well and they are not private messages or some sort unless there’s a setting that makes tweets accessible to followers only as well as the silly follower approval setting that is similar to the approval settings for new group members on Facebook.