Not true. PC won the NIT in 61 and 63; when it was considered the premiere tourney.
You've said this before, and you're still not really right. I know the recieved wisdom is that the NIT was more presigious for a while (and it was), but by the early 1960s that had already started its decline, since conference winners were forced to accept NCAA bids starting in 1950.
In 1961, Cincinnati beat a Jerry Lucas led Ohio State for the championship. In the
final AP poll before the NCAAs, Ohio State and Cincy were #1 and #2. None of the NIT teams were ranked.*
Similarly, in 1963, Loyola (Chicago) (in one of the most important tournaments ever) beat Cincy for the NCAAs, while PC beat Canicius. Cincinnati, Duke, Loyola (Final Four teams), Illinois, Mississippi State, NYU, Colorado were all ranked by the AP. None of the NIT teams were.*
*To be fair, the AP only ranked 10 teams from 1961-1968; however, the fact that a preponderance of teams considered Top 10 competed in the NCAAs shows that, by the time that PC won its two NITs, despite that tournament still being well regarded (and it would be for a little while longer), it was clearly beneath the NCAAs.
Also, looking at who the AP ranked and who missed the NCAA, you would have expected some better teams in the NIT--but by this point they seemed to be picking Northestern or Catholic teams over the likes of Duke and UNC (in 1961--both ranked in the Top 10).