This is an oddball bug. I suspect it's not fixable.
I used iOS Reeder to share a Facebook post.
Problem was, when I last used Facebook I used it as one of the Pages I maintain. That's how Facebook Pages work; you assume the Page identity while you post to it. Then you flip back to your own identity.
So Reeder shared my personal post on my public Page. It wasn't too embarrassing, but it was clearly wrong for the Page (org).
It's a weird bug; I suspect the flaw is in Facebook's API. It probably isn't designed for this use case. I also wonder if this is a side-effect of Facebook introducing the Timeline to my personal account.