You're right that Rinoa tries to put it on Edea, but Edea never makes Rinoa put it on. Just look at the pictures of the FMV:

http://www.ffshrine.org/ff8/ff8_fmvs...-edearinoa.php

You can see all Rinoa has on is that same neclace she's always wearing, the one with the ring. She's been wearing that since you first met her, as seen in the dance FMV:

http://www.ffshrine.org/ff8/ff8_fmvs...1-thedance.php

So I'm afraid you're wrong there.