Not sure 1916 should really be a candidate ... I'm guessing people are using the thought process that Wilson is remembered as a racist, so he must have done horribly with Black voters ... but he did better than any Democrat before him, IIRC. This is well past the time of Black voters being completely loyal to the GOP.
Probably because 1916 was fairly close in the Electoral College. Did Missouri have Jim Crow laws in place at that time? Wilson only won by four points here and 18 electoral votes were at stake.