You're not much of a soldier.
A US Naval vessel is sovereign US territory, as is a US military base, or a US embassy.
If you are born on a US Naval vessel to two US citizen parents, you are considered a natural born citizen by the US. But if that naval vessel was in Canadian waters, then Canada also considers you a Canadian citizen. Does the fact that Canada conferred citizenship to you make you a non-natural born citizen?
In other words, I recognize that the vessel is US territory, as you are a natural born citizen. However, the issue is that Canada also considers you a Canadian citizen as you were born in their waters (their law specifically exempts embassies only - not bases nor vessels).
So this is the perfect example of dual citizenship for a natural born citizen. Yes, it can happen, and no having dual citizenship should not disqualify a person from being President, because the person has ZERO control over what another nation considers their status as a citizen of their nation.
Actually none of them are. If a foreign national were to give birth on a U.S. Naval vessel or a U.S. military base in a foreign country or in an embassy then their child is not a U.S. citizen. Which they would be if any were actually sovereign U.S. territory. Children born overseas on a U.S. military base are natural born citizens because one or both parents are, not because they're born in a military hospital.