Since 11 of the 16 states in 1800 chose their electors by vote of the state legislature rather than of the people, there wasn't really a "popular vote" of the people in that year.
I cannot imagine that the Founders meant the clear intent of a state's vote to be voided because of a minor paperwork error. It wasn't like there were two sets of electoral votes that needed to be chosen between as in some later elections.
They were the founding fathers...
...and it appears they wasted no time in getting down to the real business of politics - searching for partisan advantage, blaming the other guy for everything which goes wrong, and arguing about everything.
That's why I referred to that disagreement on this thread.