I don't think winning the NIT proves you are the best team left out at all. Your resume is cut off on Selection Sunday. I agree that the "best" teams left out, the most talented teams, are probably high majors. But it doesn't mean they were more deserving of the bid. Just like if the stat was the opposite, that wouldn't be proof that they should have been in either.
Over the last 9 years, only one #1 seed (Minnesota in 2014) has won it. So none of the winners are even coming from the group of teams that were on the bubble. Judging anything about the winner (other than the fact that the teams who actually had a shot at the tourney don't seem to care at all) seems pointless.