Some Twitter clients, like Twitpic, only let you read and compose tweets on your timeline, not offering access to Direct Mentions (DMs). But if you still want to send someone a DM on these services, just use the old SMS code.
Security consultant Egor Homakov wrote about a neat workaround he found to post DMs to friends on Twitpic:
But you know what's really cool? ANY app can send a DM on behalf of your account, by sending to API "d NAME TEXT". I just tested with Twitpic, as you can see it doesn't require any DM permissions.
Homakov also reasons that this is a bug, since an app is supposed to have read and write permissions for DMs, so Twitter might just plug this — but it was working fine when we last checked.
How to send DM on Twitter w/o permission [Egor Homakov]