Of course, Twitter can prevent the use of any of their trademarks, making branding difficult, to say the least. Sure, you could make an unofficial Twitter client without any problems, but Twitter might be able to take legal action if you state anywhere that it's a "Twitter client."

Plus, these cat-and-mouse games require a user base that is fairly quick to update; if Twitter blocks one avenue (and they will try desperately to do so if one of these clients gains a decent number of users), an update for the client is likely necessary. I would think the easier way would be for users to get their own API keys and secrets and enter them into the app.