I are not no lawyer, nor do I play one on the telebishion thingy, but that never stopped me from expounding before, much less with open invitation such as yours, Kimberly! :)
So many interesting questions arise with this administration that never before needed consideration. It's like releasing arduously-tested software to the public and the first idiot* user finds all the bugs by pushing buttons in ways never imagined. Nobody ever ran things this wacky way before, so we never ran into these glitch-makers.
Here's a copy of the Constitution.
Here's Article 2: The Presidency
Of course, the wording of that forgotten, indecipherable, anachronistic relic of dead white Euro males is clear as can be: "No person except a natural born citizen, or a citizen of the United States, at the time of the adoption of this Constitution, shall be eligible to the office of President." (Er, actually, looking at it, the comma placement could be construed to mean one had to be natural born prior to adoption, hence nobody born since could be a citizen. Common sense would not suppose the authors intended such a self-defeating interpretation, but under some judges, who knows?)
Anyway, it seems the Constitution does not require that the Sec of State, Speaker of the House, or even Vice-President (absurd as that seems) has to qualify thusly. Could we, then, have a "successor" to the office who cannot legally succeed? Apparently. As the best lawyer I ever knew once told me, the only thing Law and Logic have in common is the letter L.
Constitutional requirement notwithstanding, it would seem most prudent — in case of unfortunate necessity, most expedient — to extend this qualification implicitly to those in the line of succession, especially to the VP, as the Founders presumably presumed thinking citizens would presume!