As for Woodrow Wilson, his mother became a "citizen" when she married her husband who was a citizen, by way of a Congressional Act of February 1855, which stated,
any woman who might lawfully be naturalized under existing laws, married, or shall be married to a citizen of the United States, shall be deemed and taken to be a citizen. [Act of February 10, 1855, 10 Stat. 604, section 2]
This act was enacted in 1855. Woodrow Wilson was born in December 1856. Therefore, Wilson would have been born to two citizen parents...on U.S. soil and therefore an NBC.
Arthur’s parents were married in Quebec. His mother was a native of the US—I wonder if she lost her citizenship by marrying a foreigner in another country.
Thanks for the details about Wilson. I know about Arthur having haunted the eligibility threads for more time that I should have...