There's a lot of people getting tied in knots here over copyright (not copywriting - it's not even close to being the same thing!).
The situation is very clear if you care to do any homework on the subject at all. You'd be well advised to take heed of what Shyflower tells you.
Any written or spoken piece of work in general carries the copyright of the original author/speaker automatically. This applies equally to interviews as they are creations of the TV company or media company that conducted the interview originally. No piece of work can be recreated, either in text from the spoken word or otherwise without the written permission of the copyright owner.
Speculation and opinion on a legal matter like copyright is not always helpful. To avoid your very own court case, do your homework and get proper advice.
In this case, you need to contact the broadcaster to see who owns the copyright on the programme you saw the interview on. This could lead you through two or three media companies until you find the right people and even then they could deny you permission to use the transcript. They might also want to see your transcript version to check for accuracy before allowing you to use it.