And how did the original founders say we should verify natural-born citizen status?
The mechanism is up to the judgment of the electors (and to the judgment of Congress when certifying the electoral result). My point is that the electoral college was created as one of many buffers to screen out lawless mob rule while still allowing the citizenry to control the state — the people in that office were clearly expected to exercise that function by (for example) withholding their votes from a candidate who was (in their determination) not legally eligible to assume the office.