I don't know if i've ever heard of a team turning down a NIT bid. Did those teams really think they deserved a NCAA Bid?
Up until the one year they accepted, Rutgers turned it down several times.
Some of the years, they might have thought they belonged in the NCAA dance, certainly the year they went to the WNIT they thought so. Other years, not necessarily, that wasn't ever Vivian's reasoning.
Her reasoning (expressed whenever we were on the bubble, even when we got in the big dance) was sometimes due to injury, or senior laden team (chance of injury), or other "semi-legit" reasoning. Otherwise, it was just that if you were not good enough for the National Championship, why would you want to play in a tournament of als0-rans? If you couldn't play well enough to earn your way to the goal, why take the consolation prize? Eventually, the AD took the decision out of her hands.
As to the WBI mentioned above, that is a "less said the better" tourney.