When in doubt always read the rules... from the Comprehensive Rule Book 4.0 Page 13 under losing the game

"A player loses the game if his Ring-bearer is killed (see overwhelmed), unless he uses game text allowing another character to carry on as Ring-bearer.
Many versions of Sam may become the Ring-bearer if Frodo is killed.
When a new character becomes your Ring-bearer, he is not wearing The One Ring, even if the old Ring-bearer was wearing it when he was killed."

Now you can go to them and point it out and let them argue about it all they want. You have the proof that your interpretation is correct.

Sit in a corner and rock back and forth while crying softly?

No seriously, I like making sure that all the rules are followed correctly and usually I do a pretty good job of remembering what they are and then interpreting them in odd situations. Bib is another good rules resource. Even though he doesn’t point out the page in the rules where the ruling can be found, he has only been wrong once or twice (assuming he is the same person as on D’s boards) so he gives correct rulings consistently.

I to know where to find the rule. Thus, I post the pages or direct quotes so people have proof to show others when trying to back up their argument.