That's still weird nonetheless... Maybe it's still 100% random ? In MP, only the player who received the pyramid is teleported, so one would think that the character with the pyramid would be the one to initiate conversation in this particular case.
I totally understand the issue though. I am clearly making one of my char the "social" guy. The other is then free to get things like Know It All and not put a single point in Charisma or whatever. =)