Don't be ridiculous, it doesn't work that way.
Smith needs to prove he traveled to Kenya if he wants people to believe his BC story and so far he's not doing a very good job of that.
I've been to Ukraine three times. I can prove this by showing my passport stamps, various photos around obvious landmarks, train tickets, etc. I can't prove I've never been to Russia. I have no photos, stamps, etc. but the absence of evidence doesn't prove I've never been there. Maybe I snuck across the border, planted my feet in Russian soil and scurried back?
I can't prove I've never been to Brazil. Or Antarctica. But I've never claimed to have visited these places.
Call me crazy but if I were to claim to have traveled to Kenya where I received a physical document that could possibly result in the removal from office of a sitting U.S. President, I think at the very least I'd provide evidence I actually visited Kenya. I dunno... Maybe of photo of myself in front of the Coast Province General Hospital waving his birth certificate in the air or something? Certainly I'd expect people to ask for some kind of proof. I'd expect people to say, "Dude, you just typed that up." and I'd want something that proves I didn't.
Fortunately for Smith, there's a whole legion of people out there who will believe anything that claims Obama was born somewhere besides Honolulu. No proof required. Heck, I could sit here at my computer and type up a bogus BC that says Obama was born in China and there'd be a million people on the internet calling me a patriot and attacking the "Obots" who doubted me.