In 1948, Kentucky’s first title, there were eight schools in the tournament. They had to beat Columbia to get to the final four (all three games they played that tournament were at MSG), Holy Cross to get to the championship game then Baylor to win it all.
In 1949, when they won their second, there were also eight schools in the tournament. They beat Villanova, then Illinois to win the “east” (again at MSG), then traveled to Seattle a week later to face Oklahoma A&M (now State).
We can make an exceptionally valid case that those two titles are what separates UK from us at this point in accomplishments. By the way, UK’s best player then, Alex Groza (brother of NFL hall of famer Lou Groza) was banned for life from the NBA as he and a couple other UK players were involved in point shaving during the 1948-1949 season (second title). It would not be unreasonable to call at least one of UK’s first two titles into question.