So yes, it lets people shoot themselves in the foot; yes, people will most likely shoot themselves in the foot; but no, that's not the main problem and in fact you can hypothetically use twine + twitter in a more or less private manner.
The problem is that broadcasting through Twitter makes you depend on a service by a company, where you could just as easily have come up with a solution that works with a publicly-known protocol which can be deployed by many parties (the closest match here would be status.net).
Then again, their point is precisely to make using the bloody thing easy. It's increadible how the easy way to make things usable always implies lots of trade-offs in security, privacy, openness and whatnot... No wonder people who solve usability problems the right way are so valuable.
[1] DEFCON 18, "Web services we just don't need": http://youtu.be/mbZccSwgbIU (it runs almost 1h, and is equal parts hilarious and pointless).