As a citizen of both countries, Brett Hull could have played in international hockey tournaments (Olympics, World Championships, etc.) for either country. The International Ice Hockey Federation, though, has an important rule that only allows a player to compete for one country in his lifetime. So once Hull decided to compete for Team USA, he was permanently ineligible to compete for Team Canada.
It seems practical for a U.S. law -- or even an amendment to the U.S. Constitution -- to be drafted in a way that contains some kind of clarification for presidential eligibility.
The well-intended provision has clearly outlived its usefulness. It might have prevented a President Maximilian I. But it didn't prevent a President named Hussein (can you get any more foreign than that? Islam has been at war with the US since the days of the Barbary Pirates)! Even the strictest construction of it would not have prevented, say, a President Billy Ayers.
If you can't depend on the judgment of the voters, what's the use?
The Founders failed to define NBC. So, now, the provision is just an excuse for any random whack job to invent his own theory of what NBC means and play politics and concern-troll (get a declaratory judgement) with it.