As per this answer, since the fixing of the calendar (let's say, at the time of the gemara), Yom Kippur does not fall on a Saturday night.
Leon Wieseltier, in his book "Kaddish" (page 102) tells of an argument between Jacob Tam and Meshullam Ben Nathan regarding whether one is allowed to eat on Shabbat afternoon. It is discussed by Zedekiah the Physician (identified on page 66 as a contemporary of Isaiah of Trani, both living in the 13th century).
Zedekiah also reports that "there was once an incident in Lorraine [where it was customary to refrain from eating on Sabbath afternoons], and there was danger [because the fast of Yom Kippur was to begin at sundown], and it was only with difficulty that permission was granted to eat on the eve of Yom Kippur just before the service began.
A page later, Wieseltier writes that Mordecai ben Hillel (Germany, 13th century) records that "it was Jacob Tam's father -- Meir Ben Samuel, or Meir the Venerable, who was married to Rashi's daughter and was one of the earliest Tosafists, or glossators on the Talmud -- who reported the incident in Lorraine, which must have occureed in the eleventh century."
There is no specific date given for the unsourced anecdote (and I don't have Zedekiah's original text to check in) but a quick look online shows that the Jewish community of Lorraine dates to AFTER the time of the gemara.
If this anecdote is accurate, the community in Lorraine, many hundreds of years after the calendar assured that "lo adu rosh" had a situation where Yom Kippur was on a Saturday night/Sunday.
Is the anecdote wrong or were there communities that didn't abide by the fixed calendar?