Maybe there were no questions because Arthur's status as a Natural Born Citizen was accepted as fact due to his birth on US soil and his mother's citizenship.
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Maybe that's what they thought. Maybe there was no indication that his father was a foreign national. Who knows. You'd have to ask the folks around then what they thought...or what they didn't think because of what they didn't know.
Yes, perhaps Arthur's father obtained his US citizenship in secret when Arthur was 14 and people didn't gossip way back then. Not likely, but, I suppose possible.