Yes, they would own the copyright on the elements of the video that they produce. They wouldn't automatically own the copyright on any statement you made. The papers you sign would probably contain language much like the language on a random forum's ToS, discussing an irrevocable, non-exclusive, limited, global license to use any statement you make and/or to license the clips containing your statements out to partners. I've never been on TV, so I don't know. While it is possible that they try to get you to transfer the copyright to any statement you make, the courts are generally pretty dubious of such attempts.
Also, giving a presentation to thousands of people, whether at a conference or over a broadcast, is at least perceived a lot differently than leaving a comment on a message board, especially if it's a small one or a niche community, so different things are shared.
Suppose one is foolish as an 18-yr-old and posts on a forum most browsed by his friends, "Ha! I just got Lifelock and since I know you can't do anything to me when I have that, my SSN is 999-99-999. Just try to steal my identity!" Suppose the IA saves this statement. The OP would have a copyright interest in it and would be within his rights to point out that the IA has no privileges that entitle it to rehost that content, so please take it down. That is totally fair.
There is no reason that copyright law should only be usable by media conglomerates that mostly use it to stop the spread of free culture and not by private individuals trying to clean up some of their past mistakes.