Yeah, if it's just for one program, I'd just contact the publisher for a pristine copy and play that. It'd be 100% legal, and would probably cost less money (and certainly less time) than trying to record it. If it's a local documentary, they'd probably be thrilled that someone would want to purchase or license it. And you wouldn't have to worry about a possible (slim, but possible) cease and desist order.
Don't believe everything on the Interwebz! A duck's quack DOES echo!