I don't know why Rutgers withdrew from the relay but Rutgers was unlikely to win. The top 7 teams finished with faster times than the Rutgers school record that was set two weeks prior. The winning time was 3.62 second faster. The record was set by a foursome that did not include Griffith. The Rutgers best time is not in the top 40 nationally.
Rutgers did make the finals in the 2016 outdoor 4x4 with both Griffith and Brown with Brown running a 44 second split. If Griffith is added there should be some improvement but I don't think enough.
I also think there has been a specific plan to get the most from Brown and Griffith in the 400 meters. Brown had run only 2 400 meter races this season prior to the big ten, running mostly 200 and 60 meter races. Griffith had a very light competitive schedule prior to the big ten.