The Party is not displayed in the party search if "Accept Party" is unchecked.
Ahh ye that's right, I clearly don't party enough Well one thing that'd be nice is turning the refusing invitations from the party settings screen and not just when someone asks to join your party in a mission map or a dungeon.
I would've been fine with automatically made parties solely because I always forget to make one so no one can join me! But either way goes, guess it's cleaner this way.