Explain this confusing SAT math problem?

Help with this question would be much appreciated! The answer is supposedly A, but I don't get it.

Jackson: 10
Callan: 5
Epstein: 8
Liu: 6
Benton: 8

The table above shows the number of consecutive nights that each of five families stayed at a certain hotel during a 14-night period. If the Liu family’s stay did not overlap with the Benton family’s stay, which of the 14 nights could be a night on which only one of the five families stayed at the hotel?

A) The 2nd
B) The 4th
C) The 5th
D) The 8th
E) The 10th

Jackson family must get to the hotel on the 1st, 2nd, 3rd, or 4th night if they stay for 10 days consecutively in a 14 day period. This means that they have to be at the hotel on the 4th, 5th, 8th, and 10th (choices B-E) no matter what. By necessity, then, at least two families will be at the hotel on all four of these dates. This is because the Liu and Benton family do not overlap, so one of the two is there on every day of the 14 day period.

The answer has to be A because it's the only night that the Jackson family might not be at the hotel along with either the Lius or the Bentons (the one family staying on that day could be either of these two).