I don't believe this is accurate. The tournament manual's only statement about the regional host institution is the following:
Regional hosting parameter: A team may be assigned to a regional site where its institution is hosting, provided the team has not played more than three regular-season games, not including conference postseason tournaments, in the arena.
Key word is "may". Oregon State was the host institution of the 2019 Portland regional, but Oregon was the #2 seed in Portland while Oregon State was the #4 seed in the Albany region.