That isn't a bug.
Per the Comprehensive Rules Document 3.0
"Many versions of Sam have a special ability that is a response action you may use when Frodo is killed (not corrupted). If Sam is in play at that moment, this allows you to transfer the Ring to Sam, and then he becomes your Ring-bearer. Sam is considered to be bearing The One Ring (not wearing The One Ring) regardless of whether Frodo was wearing it before being killed."
It will only trigger if Frodo was the ring bearer.
Someone in the Game Hall just asked about this. I initially told him the same thing you said, that it will only trigger if Frodo was the Ring-bearer... HOWEVER when I actually looked at that CR document that you quoted, as far as I can tell that CR never says that Sam only triggers if Frodo was himself the Ring-bearer. Here's the section in its entirety:
What happens when he is killed?
If your Ring-bearer is killed (even if he is overwhelmed), you lose the game.
Exception: Many versions of Sam have a special ability that is a response action you may use when Frodo is killed (not corrupted). If Sam is in play at that moment, this allows you to transfer the Ring to Sam, and then he becomes your Ring-bearer. Sam is considered to be bearing The One Ring (not wearing The One Ring) regardless of whether Frodo was wearing it before being killed."
I don't see anything in any of that that says Frodo must be the Ring-bearer in order for Sam to trigger his text, and transfer the ring.