A few questioned his place of birth. Donofrio showed this via newspaper records from the time. IIRC, nobody questioned the fact that his father was a foreign national when C.A. was born (I would assume because nobody knew his fathers status at the time or had reason to question it), who didn't become naturalized till C.A. was 14 y.o.
As far as why didn't they define the term then...that is a question for those around at the time. I would assume because the general public at large were unaware there were questions surrounding C.A. eligibility. Therefore, there was no need at the time.
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.