There was a time when you were allowed to choose - until, in 1970, Marquette chose the NIT; I am assuming the school figured it would get three home games and make more money because of it (this was before the current massive TV contract for the NCAA tournament, although half of that money goes to the conferences and another third goes mainly to the football schools as it’s based on the number of scholarships, heavily weighing those past 150).
Ever since then, the NCAA came up with a rule: “If you are invited to an NCAA championship tournament, you have the right to refuse, but if you do, then your season is over.” (For example, the Ivy League will not accept any invitations to the FCS football tournament.) There is one exception: you can schedule a “regular season” game that takes place after the tournament begins, as long as the date, location, and teams involved were scheduled by the start of the season. The only one I can think of is the annual Grambling-Southern football game. Note that the rule does apply to the MEAC and SWAC football champions in that if one or both are chosen to play in the NCAA FCS tournament, they cannot refuse and then play in the Celebration (formerly Heritage) Bowl.