However that doesn't account for State laws which, many are explicit -- the country in which you reside. I know that isn't how it works in practice, but technically, if you aren't a resident, you aren't a resident -- regardless of your parents.
Correct. But you don't need to be a physical resident to vote in a state. (Nor can you pick a state at random.) Here's what the government says, from https://www.fvap.gov/citizen-voter/additional-info :
> Citizens residing outside the U.S. may not arbitrarily choose which State to declare as their legal voting residence without meeting the State's residency requirement. The following are basic guidelines to follow in determining voting residency:
> * Your "legal State of residence" for voting purposes is the address where you last resided immediately prior to your departure from the U.S. This residence remains valid even though the citizen may no longer own property or have other ties to their last State residence and their intent to return to that State may be uncertain.
> * Voting in an election for Federal offices only may not be used as the sole basis to determine residency for the purposes of imposing State and local taxes. If you claim a particular State as your residence and have other ties with that State in addition to voting, then you may be liable for State and local taxation, depending upon that particular State law. Consult your legal counsel for specific questions or situations.
The qualifier "for voting purposes" is why there's no fraud.