Show me in what you posted where it says that the appointed electors are given the authority to interpret and apply the NBC clause in any way???
Uncle Chip, the Constitution authorizes and empowers electors (and no one else) to choose our presidents. The Founders entrusted that power to electors and to no one else.
The Constitution also establishes eligibility standards limiting the electors' choices. The Constitution thus requires the electors to interpret and apply those standards so that they can perform their president-selecting function.
Does that seem overly complicated or mysterious to you?