Allow blocking direct messages from people I don't follow

As far as I know, Twitter doesn't allow people you don't follow to send you a direct message.

My guess (which could be wrong) is that you're actually getting track alerts on your phone. Would you happen to know if you've set any track alerts on?

By definition, Track sends you a copy of any tweet that contains a keyword that you're tracking, whether or not you're following the person who sent the tweet.

The best way to confirm this is to see if the name of the Twitter user is in parenthesis.

For example, if I were tracking the word "direct" and you had sent the title of this page as a tweet, I would get an SMS notification that looks like this:

(echeng): Allow blocking direct messages from people I don't follow

Twitter uses the parenthesis around the user name to indicate that it's a track alert.

You'll find a detailed description of Track here:
http://help.twitter.com/index.php?pg=...

Hope that helps.