When it comes to its ability as a Twitter client, the People Hub is somewhat limited. When viewing someone's contact page on your device, there has always been an option to publicly mention someone on twitter (e.g. @username). However, there has been no option to send direct messages. The only way to send a direct message without installing a third party app has been to use Twitter's text message integration.
However, there is another way to send a direct message to one of your contacts using the People Hub. If you tap on the "mention on Twitter" option, a status dialog opens up with the recipient's username prefixed with an @ symbol. All you have to do is change the @ symbol with a letter D followed by a space, i.e. "D username message".
This works in both Windows Phone 7 and Windows Phone 8.