I'm sure they don't feel like spending the time to build a quality bow just for a quick segment in a low budget TV show. Just throw something out there that will sling out an arrow once or twice.
Like cooking shows, they mix the ingredients, set it aside, and then pull the finished product out of the oven. They don't have time to wait on sinew to dry. I don't blame em. They weren't filming for PA. They probly did that whole thing in the same day. Its a TV show.