After a quick glance I would say:
Change the relationship from activities to firm to only use the _firmsID and NOT the peopleID as well. That should fix it!
I agree that that relationship looks wrong, but I don't agree with the proposed fix. I think you probably should have kPROJECTSactivity_people Table Occurrence linked to the kPROJECTSactivity_FIRMS TO.
Thanks for the help.