onodrim

Yep, they basicially got it. Frodo never fully recovered from all his wounds, both emotional and physical, and so he could never be fully happy in Middle Earth again. Therefore, he was allowed special passage to the Grey Havens (kinda like Heaven for Middle Earth), along with Bilbo, the other ring bearer. It's true that it didn't alter him. However, he was a ringbearer for a short time, so at the end of his life he was also allowed to join Frodo at the Grey Havens.

__________________
"The world is so exquisite with so much love and moral depth, that there is no reason to deceive ourselves with pretty stories for which there’s little good evidence. Far better it seems to me, in our vulnerability, is to look death in the eye and to be grateful every day for the brief but magnificent opportunity that life provides"
-Carl Sagan