Apples and oranges. You have video proof of Kerry throwing away his medals, smearing the troops, and his fellow servicemen telling you he is untrustworthy. Unless someone comes forward with some pictures of Obama in some Mombasa hospital delivery room, this is never going to be more than unsubstantiated rumors.
He can prove it by showing his birth certificate. He has to prove it, he is the president, not me.
Kerry may have done those things to smear the troops on film, but it was investigations that showed that his heroic claims were not true.