I can see why they would have been paranoid about that, but is the natural-born citizen rule as constituted in the, er, Constitution, a reasonable prophylactic? For one thing, it didn't apply to anyone born before 1787, which must have applied to many of their potential sleepers; for another, there's no obvious reason to think that natural-born citizens are less likely to favour royalism than immigrants - who have, in many cases, fled from oppressive royalist tyrannies. For example, someone born in Nevis (like Alexander Hamilton) would today be ineligible, whereas someone born in Connecticut (like Benedict Arnold) would be A-OK.