1. Natural born US citizens make no such oath and make up far more a percentage of the population than naturalized citizens.

2) Many countries do NOT allow their citizens to legally renounce their citizenship, so no matter what "oath" a person makes they are still considered a citizen of the original country.

3) As you have stated, no one actually asks for proof that ones original citizenship has been renounced, this is basically because of (2) posted above.