There is an icon the you select, which brings up a small menu where you can change the party open status. Put your pointer over the two icons above your name. One will say show invitations and right next to it (which will have two shoulder to shoulder characters) it should say fireteam privacy. That's the one you want.

Yeah, I tried that before. Sent a message to the guy, took 3 minutes with this wonderful PSN messaging system. Got his reply after 5 minutes saying it was ok for me to join, needless to say, he had already finished the mission by that time... Now I just join directly. If they're not happy, they boot me (happened before and that's fine by me).