I don't think the person misunderstood. I think they did realize that what they were saying was public, but didn't care too much - they just wanted to get a mes

I don't think the person misunderstood. I think they did realize that what they were saying was public, but didn't care too much - they just wanted to get a message to a specific person, and Twitter made the easiest way to do so to say it publicly. As a result, a lot of such messages ended up being public, and while each of them was innocent, all of them taken together were saying a lot about that person. And the latter may have been an implication that the person didn't realize.