Based on the facts you presented before, I can't imagine that you could possibly lose this case. Furthermore, this neighbor sounds crazy enough to jump at the chance to be on television.
As long as you maintain your cool and present yourselves as reasonable adults (with lots of documentation to back your case), the neighbor is probably going to make a fool of themselves on national television.
There are many things that I wouldn't go on television over, but I wouldn't view this as being particularly personal or embarrassing. I'd probably do it.