That margin of error is across the whole country. Vote checking would run over a much smaller area.
It doesn't matter if it's across the whole country because the identification incorporates zipcodes. All ambiguities are local to a single town.
agreed and upvoted.
This would be to find those multi-registered voters. Considering the current system is merely first + lastname, I think either approach above would be superior and without leaking SSN's to yet another government database.