Huh! Indeed? Now why... Grishnakh didn't bite off Frodo's arm... nor did Sam sing lullaby to him... nor did he eat the Ring (though he'd certainly like to... bah! maybe not, what would Sauron do to him then if he learned it's inside him?)... not personal, you say? But what then, when they are connected by it? Grishnakh captured, or later also saved Frodo's friends, Merry&Pippin... could it be said that Carcharoth "saved" the Silmaril? Or those who killed him were his friends... Horsemen - Huan? Bah, hobbits did not know the Horsemen... Mablung... I can't think of anything, really.
Maybe - a Nazgul that scared Frodo was supposed to carry Grishnakh over the water? But Carcharoth did not need anything to carry... and the simple relationship Frodo - Sauron - Grishnakh vs. Beren - Morgoth - Carcharoth it's not as you said... that idea would fit more with Shagrat or some other "door guard".