I agree with your point. Third parties must have no control. However the real demons at play here when we are in pursuit of 'truth' is ourselves. We are the most likely to want to revise our own history and for the purposes of truth we ought not allow that beyond mere moments after the note is signed.
Discussion
I'd disagree if you also mean the ability to delete. As of now, I think people should be able to delete notes. My opinion could change on that, but I do already understand the reasons why one would NOT want that ability to exist, as you've already pointed out. It has pros and cons in my mind.