Madison said this regards to a William Smith from S. Carolina born in 1758 and who left the colonies in 1770 as a child. He was in England at prep school with his parents and they were all absent from America during the whole of the war until November 1783; his parents both died while they were in England.
During the time of Williams' absence, the American Revolution took place in 1776. The debate in 1789 in Congress ("David Ramsay vs William Smith" -- S. Carolina)revolved around in order to his becoming a Citizen of the US, AS WELL AS be allowed to serve in public office at a US Representative ("seven Years a Citizen of the United States"), Williams must have done something previously on his part to show his acquiescence in the new US government established without his consent by the "Declaration of Independence".
In the end, Williams was "granted" citizenship and his Congressional seat, somewhat because of his political power, confusion over S. Carolina laws, and AT THE TIME, there was no existing case law to fall back on. HOWEVER, born out of his situation and other was the Citizenship Act of 1790 and others.
There ARE some striking similarities between BHO and Williams though. Those who opposed his citizenship and right to be a US Representative questioned his "locality" as an 18 year old in England at the time during the "Declaration of Independence".
ALSO, there were those who questioned his LOYALTY -- was it to the US or England?
A final note: Williams COULD NOT have served as US President, despite his birth in S. Carolina, because of the "out clause" written by the Framers AS WELL AS the Residency requirement for POTUS as outlined in the Constitution:
"No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States. "
I think, though, that you are in error in referring to "William Smith" as "Williams."
Unfortunately, today's Congress is not as concerned about constitutional qualifications of officeholders.