I'm sure about that at all... Throne Room modifies Fishing Village in that it causes it to be played twice, instead of once. If "return to your hand" counts as modification the same way, then how do you define "that other card also stays in your play area until it is no longer doing anything"... it returned the FV to your hand, it's not doing anything anymore. It has no effect on what will happen on your next turn at all. Playing the FV a second time affects your next turn, but playing the Believer doesn't at all.
I'm saying that if you play the Believer on a FV that you played this turn, the Believer would stay in play because it modified the FV in such a way that a reminder is warrented. Technically the Throne Room isn't "doing anything" except serving as a reminder. The Believer would serve as a reminder until your next turn when the FV that it returned to your hand has finished it's effect.
Yes, the word "also" is out of place because the FV would no longer be "also" in play, but when seaside was made, there were no published cards that could remove a duration from play, but as we see with Procession, even though it trashes the Duration card, Procession "also" stays in play.
If you want to argue that TR and Procession are "doing something" because they are the means of actually playing the duration card, then why would the rule even include "or modify"? It seems clear to me that if any card you play "modifies" a duration card in play such that you'll need a reminder for the next turns effect, then that card stays in play until that next turn effect happens, then it's discarded during that cleanup.
EDIT: re-reading the previous comment, I think I should clear up that I'm saying the Believer would stay in play only if you use it to return a Duration that you played
this turn! If you are returning a Duration that's already been in play since your last turn and already had its next turn effect, the Believer would not be "doing anything" and would be discarded as normal during cleanup. I'm hoping that was the only disagreement.