If you do not want your information aggregated across the web then make it password protected and do not allow access to people who have not accepted your terms of service. You are actively publishing text written by someone else (not even by you), and placing it in public places. Trying to claim some type of ownership on that question is counter to the principles of the web and shows to me that your need for profit is more important than your principles.

And then following it up by publicly lambasting a figure rather than privately clearing it just seems like a desperate tactic to gain publicity.

That's just silly. There are only so many ways to ask "Why is the sky blue?". In 140 characters it's a little difficult to get creative enough to make a question copyrightable. And once it's in the Twitter-verse, there is no controlling what is done with it.

If they were to have someone monitor the feed, make minor changes, and post to their own site would that be acceptable?