You're right if by correctly you mean not like this. The 'correct' way to do it would be to indicate that the field is editable. Once the user has clicked you can enable/reveal the save button if you really want it hidden. Twitter's tweet box is obviously an editable form element that can be clicked on.

It is ok if clicking on an element enables additional contextual actions… the problem is that we don't look at a page with our mouse pointer. The pointer is a proxy for our hand not our eyes.

It helps when the activation hover area is large: anywhere over a tweet, all new per-tweet options appear.

I'm not sure I agree. It completely breaks on tablets for one thing.

Does not have to though, Tweetbot's UI behaves nicely in this regard. It does not have hover, but its equivalent is to tap a tweet. This opens a small "drawer" of 5 tweet-specific buttons (reply, retweet, favorite, detail and "actions", which include posting a link to the tweet, copying the tweet's content, emailing the tweet's content and translating the tweet's content).