This happened about 1949 or 1950. Either coincidentally or in response, the NCAA tournament was created. Afterward, the NIT was relegated to 2nd place. However, since only conference tourney winners and a select few independents were given a berth in the NCAAs, the NIT was often made up from very good teams. Other than perhaps UCLA, you could often argue which tournament winner was the best.

This was basically the situation when Tech was first chosen for the NIT in 1973, Previously, they had been the last team chosen for the NCAA in 1967. Having been blown out by Toledo in the last game of the 66-67 season, they had to face the same team again the first game of the NCAA Tournament. This time Tech won by one or two I think. But I digress...