Good day
your thought man is Possible and nice one but what if vermoth help the big boss with Assassination that she was the only one who can do it and she become the big boss favorite one because she prove to him that she is special that is what I thing with vermouth but if you ask me about the Gin and the others I think that they were normal people and they got blackmail by some or they murder someone and did not find a way to get out and then the big boss came and save them buy killing method. So they are loyalty to him by fear except for Gin I think the big boss like him because of his Desire to kill hehe.
Thins have good day