In 2010, when Bama was facing this situation at SC, it was being reported then that NO team in the AP poll history had faced it and won all 3 games. That turned out to be incorrect, and even this report has an error. '45 Army did not achieve it in a 3 week period. They had an open date between the second and third games of the three.
2010 Bama, of course, is one of the two that did not win all three games. 2008 Texas is the other, but they deserve an * because they played 4 in 4 weeks and won the first three, but not as #1. All they did was beat #1 Oklahoma in the first week and move from #5 to #1. They then beat #11 Missouri in the second week, and #7 Oklahoma State in the third week before losing to #6 Texas Tech in the fourth week.