Oh, I was going to say have you made sure they haven't switched back but it seem's you've done that. Sometimes it just takes a turn on and off and its sorted. Try turning all notifications off and turning the console off. Then turning everything on.
been havig exactly the same problems, last i was sending invites to my mate and he wasnt recieving them, the other day i wasnt getting any messages showing up in my inbox yet on xbox.com they were there, dunno whats going on
I had a similar problem last night also. One specific friend couldn't receive any messages or invites from me, yet could from anyone else, and everyone else was getting my messages fine. Very odd, and he hadn't blocked me or anything.