I believe they don't even have to be in the same region to both play in Milwaukee, so it's possible they wouldn't see each other until the final.
This reason is why I called them our "roommates" and not our opponents.
If we're at least a #4 seed you avoid playing any of the other Top 16 teams until the second weekend.
Anything under that level is a scrum of the committee trying to make the bracket work.