The producers aren't desperate to make a connection, they're just pandering to the kinds of people who already believe this anyway and are looking for something to reinforce their beliefs (much like the people they interview for the show itself).
As to the overall idea, I doubt it very much. On the one hand, westerners have a long history of looking down on foreign civilizations as being backwards or barbaric based on some arbitrary standard, usually something to do with technology; in point of fact, our society is not a whole lot better developed or organized than ancient civilizations of 4000 years ago, the only difference is our technology is better and our populace and infrastructure is a lot cleaner. Ancient Rome wouldn't be all that different from a modern superpower if they had mastered electricity or figured out how to make concrete, and they missed out on those innovations only for lack of development time.
The most realistic version of the theory is that some alien probe or small expedition got stranded on Earth and it was, in the end, a one-time freak meeting between two different species... on the other hand, the odds that the aliens would have had enough common ground with humans to communicate with them AT ALL is extremely slim, even if they were able to survive in our environment long enough to make the attempt, even if the humans they encountered recognized them as "beings from another world" instead of "funny looking animals carrying bits of things on their backs."
It's actually more likely that the first contact between humans and aliens would have involved a dying alien breathing his last dying gasp as an ancient hunter-gatherer watched him from the bushes wondering what he might taste like.