In 2010, UNC was coming off winning a NC, and they had a rough year going 16-16. That UNC team accepted a NIT bid, and went to the finals losing to Dayton coached by soon-to-be GT coach Brian Gregory. So, UNC has "lowered itself" to play in the NIT before.
Similarly, in 2013, when KY was at the height of their powers and coming off a Natty in 2012, they missed the NCAAT and accepted a NIT bid. Hilariously, KY could not use Rupp because the NCAAT was being played there, so KY played at Robert Morris and lost.