This was a very thinly-veiled allegory for the political happenings of the past few years, especially the birther movement. (Earth Certificates instead of birth certificates... get it?!?)
Futurama decided to go with the twist that candidate Chris Travers didn't have an Earth Certificate yet because he was from the future. Apparently the Earth Constitution doesn't have a minimum age to be president. It's a shame we do have now, because Blue Ivy Carter would be a fantastic president.
The entire story just seemed very expected. Of course the show would go for mocking birthers because it was the obvious thing to do. Leela and Bender got involved because they're