Without giving the whole story away,
Plumber #3 was on the hook the most because he didn't fully assess the problem.
When a plumber is called out to fix a problem, there has to be a degree of culpability where just a simple fix doesn't mean you don't own the situation.
It would of been in Plumber #3's best interest to test the system, find other issues and red flag it before leaving without a signed invoice...but I think even then the signed document doesn't mean squat unless you took strong arm tactic action.
I wish I brought more D-chips with me that day to tape it all, because there's a lot more to the story on this one.